Introductory statistics 10th edition weiss test bank 1

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. Assume that the variable under consideration has a density curve.

1) The percentage of all possible observations of the variable that lie between 6 and 12 equals the area

under its density curve between and , expressed as a percentage.

A) 0.06, 0.12 B) 6, 12 C) 3, 6 D) 7, 13

2) The area under the density curve that lies to the right of 15 is 0.545. What percentage of all possible observations of the variable are at most 15?

A) 79.5% B) 20.5% C) 45.5% D) 54.5%

3) The area under the density curve that lies between 29 and 46 is 0 456 What percentage of all possible observations of the variable are either less than 29 or greater than 46?

A) 45.6% B) 70.6% C) 54.4% D) 29.4%

4) Given that 33.6% of all possible observations of the variable are less than 10, determine the area under the density curve that lies to the right of 10

A) 0 664 B) 0 414 C) 0 336 D) 0 164

Solve the problem.

5) A northeastern college has an enrollment of 2835 female students Records show that the mean height of these students is 65.2 inches and that the standard deviation is 2.8 inches. The table shows frequency and relative-frequency data for these heights If you assume that the distribution of heights is approximately normal, then you can use the table to estimate areas under the associated normal curve (that is, under the normal curve that has parameters μ = 65 2 and σ = 2 8) Making this assumption, estimate the area under the associated normal curve between 65 and 70.

1)

2)

3)

4)

5)

6) A southeastern college has an enrollment of 2951 female students. Records show that the mean height of these students is 64.7 inches and that the standard deviation is 2.3 inches. The table shows frequency and relative-frequency data for these heights. If you assume that the distribution of heights is approximately normal, then you can use the table to estimate areas under the associated normal curve (that is, under the normal curve that has parameters μ = 64 7 and σ = 2 3) Making this assumption, estimate the area under the associated normal curve to the left of 61

7) A southeastern college has an enrollment of 2951 female students. Records show that the mean height of these students is 64.7 inches and that the standard deviation is 2.3 inches. The table shows frequency and relative-frequency data for these heights. If you assume that the distribution of heights is approximately normal, then you can use the table to estimate areas under the associated normal curve (that is, under the normal curve that has parameters μ = 64 7 and σ = 2 3) Making this assumption, estimate the area under the associated normal curve to the right of 63

Height (inches) Freq Relative freq

Fill in the blanks by standardizing the normally distributed variable.

8) Dave drives to work each morning at about the same time His commute time is normally distributed with a mean of 54 minutes and a standard deviation of 7 minutes The percentage of time that his commute time lies between 40 and 75 minutes is equal to the area under the standard normal curve between and

9) Dave drives to work each morning at about the same time His commute time is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes The percentage of time that his commute time exceeds 55 minutes is equal to the area under the standard normal curve that lies to the of

10) Dave drives to work each morning at about the same time His commute time is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes The percentage of time that his commute time is less than 49 minutes is equal to the area under the standard normal curve that lies to the of .

0.69, 0.85 B) -1, 0

0, 1

-2, 0

11) The amount of time that customers wait in line during peak hours at one bank is normally distributed with a mean of 13 minutes and a standard deviation of 2 minutes The percentage of time that the waiting time lies between 11 and 13 minutes is equal to the area under the standard normal curve between and .

12) The amount of time that customers wait in line during peak hours at one bank is normally distributed with a mean of 13 minutes and a standard deviation of 3 minutes. The percentage of time that the waiting time exceeds 10 minutes is equal to the area under the standard normal curve that lies to the of

right, -1

right, 1

left, -1

left,

13) The amount of time that customers wait in line during peak hours at one bank is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes. The percentage of time that the waiting time is less than 13 minutes is equal to the area under the standard normal curve that lies to the of

Solve the problem.

14) Frequency data were reported for the ages of women who became mothers during one year in a selected U.S. city. The age distribution is given in the table. Obtain a relative-frequency histogram of these data and determine whether the ages are approximately normally distributed

No The distribution is right-skewed

C) Yes The distribution is bell-shaped

B) No The distribution is J-shaped

D) No The distribution is left-skewed

15) Frequency data were reported for the ages of women who became mothers during one year in a selected U.S. city. The age distribution is given in the table. Obtain a relative-frequency histogram

15)

of these data and determine whether the ages are approximately normally distributed.

285

479

867

-under 45 1021

-under 50 225 50-under 55 56

A) Yes. The distribution is bell-shaped.

C) No The distribution is J-shaped

B) No. The distribution is left-skewed.

D) No The distribution is right-skewed

16)

10-under

-under

-under

45

227

123

C) No. The distribution is left-skewed.

B) No The distribution is right-skewed

D) No. The distribution is uniform.

Age Frequency (yrs) 20

-under

14

240 50-under

-under

24

-under 65 15 A) No The distribution is uniform

C) No The distribution is right-skewed

D) No The distribution is left-skewed

18) Frequency data were reported for the ages of full-time employees at a company The age distribution is given in the table Obtain a relative-frequency histogram of these data and determine whether the ages are approximately normally distributed.

266

300

A) No The distribution is right-skewed

C) No. The distribution is uniform.

B) Yes The distribution is bell-shaped

D) No. The distribution is left-skewed.

19) Age

Frequency

-under

A) No The distribution is right-skewed

C) No The distribution is left-skewed

B) No The distribution is uniform

D) Yes The distribution is bell-shaped

20) Frequency data were reported for the ages of full-time employees at a company The age distribution is given in the table Obtain a relative-frequency histogram of these data and determine whether the ages are approximately normally distributed.

Age Frequency (yrs)

25-under 30 23 30-under 35 25 35-under 40 24 40-under 45 30 45-under 50 26 50-under 55 22 55-under 60 27 60-under 65 30 65-under 70 19

A) No The distribution is left-skewed

C) No. The distribution is uniform.

B) No The distribution is right-skewed

D) Yes. The distribution is bell-shaped.

21) Data were reported for household size (number of people in household) in a small community

The size distribution is given in the table. Obtain a relative-frequency histogram for these data and determine whether the household sizes are approximately normally distributed

Size Frequency (# of people)

1-under 2 2

2-under 3 11

3-under 4 35

4-under 5 41

5-under 6 7

6-under 7 3

A) No The distribution is uniform

C) Yes. The distribution is bell-shaped.

B) No The distribution is right-skewed

D) No. The distribution is left-skewed.

22) Data were reported for household size (number of people in household) in a small community.

The size distribution is given in the table Obtain a relative-frequency histogram for these data and determine whether the household sizes are approximately normally distributed

Size Frequency (# of people)

1-under 2 4

2-under 3 33

3-under 4 30

4-under 5 12

5-under 6 6

6-under 7 3

A) No. The distribution is right-skewed.

C) Yes. The distribution is bell-shaped.

B) No. The distribution is left-skewed.

D) No. The distribution has outliers.

21)

22)

23) Data were reported for household size (number of people in household) in a small community

determine whether the household sizes are approximately normally distributed.

The size distribution is given in the table. Obtain a relative-frequency histogram for these data and

1-under 2 4

2-under 3 0

3-under 4 2

4-under 5 10

5-under 6 32

6-under 7 28

7-under 8 8

8-under 9 4

A) No. The distribution is right-skewed. B) No. The distribution has outliers.

C) No The distribution is left-skewed D) Yes The distribution is bell-shaped

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response.

24) For a variable with a density curve, what is the relationship between the percentage of all possible observations of the variable that lie within any specified range and the corresponding area under its density curve?

25) A curve has area 0 276 to the left of 5 and area 0 627 to the right of 5 Could this curve be a density curve for some variable? Explain your answer.

26) Two random variables are normally distributed with the same mean. One has a standard deviation of 10 while the other has a standard deviation of 15 How will the graphs of the two variables differ and how will they be alike?

27) On the same axes sketch normal distributions with

a. μ = 6, σ = 4

b. μ = 6, σ = 2

c. μ = -6, σ = 2

26)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 28) Which of the variables below do you think will be roughly normally distributed?

a Weights of 10 year old boys

b Incomes of 40 year old adults

c. The numbers that show up when you roll a balanced die

d. The amount of coffee which a filling machine puts into "4 ounce jars"

A) a only B) a and d C) a, b, c, d D) a, b,

d

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

23) Data were reported for household size (number of people in household) in a small community

29) How does the standard normal distribution differ from a nonstandard normal distribution? Why is it necessary to standardize in order to find percentages for nonstandard normal variables?

The size distribution is given in the table. Obtain a relative-frequency histogram for these data and

23)

30) A variable is normally distributed with a mean of 100 and a standard deviation of 10 30) Which is larger, the percentage of observations between 80 and 90 or the percentage of observations between 120 and 130? Explain your reasoning

31) Which is larger, the area under the standard normal curve between -1 and 1, or the area under the standard normal curve between 0 and 2? Explain your reasoning 31)

32) A variable is normally distributed. 42% of the possible observations of the variable lie between 20 and 28 What information does this give you about the graph of the normal curve for this variable?

32)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

33) The area under the standard normal curve between 1 and 2 is equal to 0 1359 Scores on a particular aptitude test are normally distributed with a mean of 100 and a standard deviation of 10 Which of the following are equal to 13 59%?

a The percentage of scores between 120 and 130 b The percentage of scores between 110 and 120 c. The percentage of scores between 80 and 90

d. The percentage of scores between 90 and 120 e. The percentage of scores between 90 and 110

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

34) A variable is normally distributed with a mean of 100 and a standard deviation of 10. A

student wanted to find the percentage of observations of the variable lying between 106 and 110 What is wrong with his solution?

Student's solution:

z-scores: 106-100 = 0 6 110-100 = 1 0

34) 10 10

Percentage of scores lying between 106 and 110 = difference between z-scores = 1 0 - 0 6 = 0 4 = 40%

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a table of areas to find the specified area under the standard normal curve.

35) The area that lies between 0 and 3 01

36) The area that lies to the left of 1 13

0.1292

A variable is normally distributed with a mean of 100 and a standard deviation of

Use a table of areas for the standard normal curve to find the required z-score.

Find the z-score for which the area under the standard normal curve to its left is

Find the z-score for which the area under the standard normal curve to its left is 0.40

Find the z-score having area 0 09 to its left under the standard normal curve

Find the z-score for which the area under the standard normal curve to its left is

57) Find the z-score for having area 0 07 to its right under the standard normal curve, that is, find z 0 07 .

58) Find the z-score for having area 0 09 to its right under the standard normal curve, that is, find z 0 09

59) Find the z-score having area 0.86 to its right under the standard normal curve; that is, find z 0 86 .

60) Find z 0.45

61) Determine the two z-scores that divide the area under the standard normal curve into a middle 0 874 area and two outside 0 063 areas

62) Determine the two z-scores that divide the area under the standard normal curve into a middle 0.96 area and two outside 0.02 areas.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response.

63) Sketch a standard normal curve and shade the area between the z-scores -2 5 and -1 63)

64) Sketch a standard normal curve and shade the area to the right of the z-score 1 6 64)

65) Suppose that you know the area under the standard normal curve to the right of -2 How could you use this to find the area under the standard normal curve to the left of 2? Explain your reasoning.

66) Suppose that you know the area under the standard normal curve to the right of1.7.

How could you use this to find the area under the standard normal curve to the right of 1 7? Explain your reasoning

67) Suppose that you know the area under the standard normal curve to the right of 2 and the area under the standard normal curve to the right of 1. Without further consulting a table

65)

66)

of areas, how could you find the area

under the standard normal curve between 1 and 2? Explain your reasoning 67)

68) Suppose that you know the area under the standard normal curve between 1 and 3 and the area under the standard normal curve to the left of 3 Without further consulting a table of areas, how could you find the area under the standard normal curve to the left of 1? Explain your reasoning by using a sketch of the standard normal curve

68)

69) The area under the standard normal curve to the right of a z-score is 0 56 Explain how you could use a table of areas to find the z-score

70) A student wished to use a table of areas for the standard normal curve to find the zscore having an area to its right of 0.52. The student started by looking for the closest area to

0 52 in the body of the table and reading off the corresponding z-score which was 0 05 She then subtracted this z-score from 1 to get 0 95 Was her reasoning correct?

If not, where did she go wrong and how would you have solved the problem?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 71) Which of the following statements concerning the standard normal curve is/are true (if any)?

a The area under the standard normal curve to the left of -3 is zero

b. The area under the standard normal curve between any two z-scores is greater than zero.

c. The area under the standard normal curve between two z-scores will be negative if both zscore are negative.

d The area under the standard normal curve to the left of any z-score is less than 1 A) a, b B) a, c C) a D) b, d

72) Which of the following statements concerning areas under the standard normal curve is/are true?

a. If a z-score is negative, the area to its right is greater than 0.5

b If the area to the right of a z-score is less than 0 5, the z-score is negative

c. If a z-score is positive, the area to its left is less than 0 5 A) a B) a, b C) a, c D) b, c

Find the indicated probability or percentage for the normally distributed variable.

73) The variable X is normally distributed

The mean is μ = 60 0 and the standard deviation is σ = 4 0 Find P(X < 53 0)

74) The variable X is normally distributed The mean is μ = 15 2 and the standard deviation is σ = 0 9 Find P(X > 16.1).

75) The variable X is normally distributed.The mean is μ = 22.0 and the standard deviation is σ = 2.4. Find P(19 7 < X < 25 3)

76) The diameters of bolts produced by a certain machine are normally distributed with a mean of

inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0 32 inches?

77) The incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation $150. What percentage of trainees earn less than $900 a month?

78) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz?

79) A bank's loan officer rates applicants for credit The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275

80) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 170 and 220

81) The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?

82) Assume that the weights of quarters are normally distributed with a mean of 5 67 g and a standard deviation 0 070 g. A vending machine will only accept coins weighing between 5 48 g and 5 82 g. What percentage of legal quarters will be rejected?

Find the specified percentile, quartile, or decile.

83) The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 201 hours and a standard deviation of 11 hours Find the first quartile, Q 1

193 63 B) 198 25

208 37

84) At one college, GPAs are normally distributed with a mean of 2.6 and a standard deviation of 0 6 Find the third quartile, Q3 .

3 05 B) 3 002

85) The amount of Jen's monthly phone bill is normally distributed with a mean of $70 and a standard deviation of $11. Find the first quartile, Q 1 .

$72 75 B) $64 5

86) The annual precipitation for one city is normally distributed with a mean of 33.4 inches and a standard deviation of 3 5 inches Find the 2nd decile

36 34 inches

40 575 inches

26 225 inches

30 46 inches

87) Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the value of the third quartile.

64 3 inches

inches

88) A bank's loan officer rates applicants for credit The ratings are normally distributed with a mean of 200 and a standard deviation of 50 Find the 6th decile

89) Scores on an English test are normally distributed with a mean of 33.1 and a standard deviation of 7. Find the 41st percentile.

A) 31.5 B) 34.7

C) 37.2 D) 29.0

90) Suppose that replacement times for washing machines are normally distributed with a mean of 8.8 years and a standard deviation of 2 years. Find the 82nd percentile.

A) 10.6 years B) 9.2 years C) 7.0 years D) 10.1 years

91) The weights of certain machine components are normally distributed with a mean of 8 53 g and a standard deviation of 0 1 g Find the 97th percentile

A) 8 80 g B) 8 58 g C) 8 55 g D) 8 72 g

92) The serum cholesterol levels for men in one age group are normally distributed with a mean of 178.1 and a standard deviation of 40.5. All units are in mg/100 mL. Find the 9th percentile

A) 107 6 mg/100mL

C) 123 8 mg/100mL

Use the empirical rule to solve the problem.

B) 165 1 mg/100mL

D) 161 5 mg/100mL

93) The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 10 hours What percentage of the bulbs have lifetimes that lie within 1

standard deviation to either side of the mean?

A) 31 74% B) 84 13% C) 95 44% D) 68.26%

94) The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 400 hours and a standard deviation of 10 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations to either side of the mean?

A) 97.72% B) 68.26% C) 99.74% D) 95.44%

95) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure that lies within 3 standard deviations to either side of the mean?

A) 99 74% B) 68 26% C) 95 44% D) 99 99%

96) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg What percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg?

A) 99 99% B) 68 26% C) 95 44% D) 99 74%

90)

91)

92)

93)

94)

97) At one college, GPAs are normally distributed with a mean of 3 and a standard deviation of 0 4 What percentage of students at the college have a GPA between 2 6 and 3 4?

A) 99 74% B) 68 26% C) 95 44% D)

84.13%

98) The amount of Jen's monthly phone bill is normally distributed with a mean of $73 and a standard deviation of $11. What percentage of her phone bills are between $40 and $106?

A) 99 99% B) 99 74% C) 95 44% D)

68 26%

98)

99) The amount of Jen's monthly phone bill is normally distributed with a mean of $66 and a standard deviation of $8. Fill in the blanks.

68 26% of her phone bills are between $__ and $___

100) The annual precipitation for one city is normally distributed with a mean of 347 inches and a standard deviation of 3 3 inches Fill in the blanks

In 95 44% of the years, the precipitation in this city is between and inches

101) The annual precipitation for one city is normally distributed with a mean of 25.9 inches and a standard deviation of 3 5 inches Fill in the blanks

In 99.74% of the years, the precipitation in this city is between and inches.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response.

102) Scores on an aptitude test are normally distributed with a mean of 400 and a standard deviation of 60 Explain how you would find any given percentile

103) Use a sketch of the standard normal curve to explain the difference between z-scores and areas under the standard normal curve. What are the possible values for an area and what are the possible values for a z-score?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

104) True or false, the mean of a normally distributed variable can be any real number.

A) True B) False

105) True or false, the standard deviation of a normally distributed variable can be any real number.

A) True B) False

106) True or false, areas under the standard normal curve cannot be negative, whereas z-scores can be positive or negative.

A) True B) False

107) Most problems involving normally distributed variables are one of two types.

Type A: Find a probability or percentage, e.g. find the probability that X lies in a specified range. Type B: Find the observation corresponding to a given probability or percentage.

Suppose that scores on a test are normally distributed with a mean of 80 and a standard deviation of 8. Which of the following questions below are of type B?

a Find the 80th percentile

b Find the cutoff for the A grade if the top 10% get an A

c. Find the percentage scoring more than 90

d Find the score that separates the bottom 30% from the top 70%.

e Find the probability that a randomly selected student will score more than 80

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

108) Suppose that scores on a test are normally distributed with a mean of 80 and a standard deviation of 8. Read the two questions below.

A What is the 90th percentile?

B What percentage of students score less than 90?

Explain the difference between the two questions Describe how the method for solving A would differ from the the method for solving B Be sure to include in your explanation a description of how the table of areas would be used in each case

109) Suppose that scores on a test are normally distributed with a mean of 80 and a standard deviation of 8. You have been asked to find the 70th percentile After sketching a standard normal curve and shading the area of interest, the next step in solving this problem is to use the table of areas Would you look for 0 7 in the body of the table or in the lefthand column? Explain your reasoning

109)

(in dollars) of a sample of 12 nurses working at a Los Angeles hospital

112) The final exam scores for 15 students in a statistics course are given below.

113) The resting heart rates from a group of 9 men before starting a workout program are given below.

114) The prices per gallon (in dollars) of regular unleaded gasoline at twelve service stations are given below.

114)

Provide an appropriate response.

115) A normal probability plot is given below for a sample of scores on an aptitude test Use the plot to assess the normality of scores on this test Explain your reasoning

115)

116) A normal probability plot is given below for the lifetimes (in hours) of a sample of batteries of a particular brand. Use the plot to assess the normality of the lifetimes of these batteries Explain your reasoning

116)

117) A normal probability plot is given below for a sample of scores on an aptitude test. Use the plot to assess the normality of scores on this test. Explain your reasoning.

117)

118) A normal probability plot is given below for the weekly incomes (in dollars) of a sample of engineers in one town. Use the plot to assess the normality of the incomes of engineers in this town Explain your reasoning

119) A normal probability plot is given below for a sample of scores on an aptitude test. Use the plot to identify outliers, if any. Explain your reasoning.

120) A normal probability plot is given below for the lifetimes (in hours) of batteries of a particular type. Use the plot to identify outliers, if any. Explain your reasoning

121) A normal probability plot is given below for a sample of scores on an aptitude test. Use the plot to identify outliers, if any. Explain your reasoning.

122) A normal probability plot is given below for the weekly incomes (in dollars) of a sample of engineers in one town. Use the plot to identify outliers, if any. Explain your reasoning

123) Generally, the normal probability plot for a data set must be roughly linear in order to assume that the variable is approximately normally distributed. Should this rule be interpreted more strictly for small data sets or for large data sets? Explain

124) In assessing the normality of a data set, why is it easier to interpret a normal probability plot than it is to interpret a histogram?

125) In assessing the normality of data, why is a normal probability plot especially advantageous for small samples?

126) When a normal probability plot is constructed, which axis is used for the normal scores (horizontal or vertical)?

127) Does the presence of an outlier in your data set necessarily mean that you cannot use the normal model to interpret the data? Explain

124)

125)

126)

127)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.

128) With n = 20 and p = 0 60, estimate P(less than or equal to 8) A) 0 4953 B) 0 0668 C) 0 0548 D) 0 4332

128)

129) Estimate the probability of getting exactly 43 boys in 90 births.

130) A multiple choice test consists of 60 questions Each question has 4 possible answers of which one is correct If all answers are random guesses, estimate the probability of getting at least 20% correct.

131) A certain question on a test is answered correctly by 22% of the respondents. Estimate the probability that among the next 150 responses there will be at most 40 correct answers

A) 0 0694 B) 0 9306 C) 0 1003 D) 0 8997

132) A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects.

133) In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions A) 0 8962 B) 0 0420 C) 0 1038 D)

134) The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate A) 0 0669 B) 0 0769 C) 0 0679 D) 0 9331

135) Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, exactly 225 are defective.

136) Two percent of hair dryers produced at a certain plant are defective Estimate the probability that of 10,000 randomly selected hair dryers, the number of defectives is between 195 and 210 inclusive.

0.4251 B) 0.3989 C) 0.4034 D) 0.4017

137) Estimate the probability that in 200 rolls of a balanced die, the number of sixes is between 36 and 45 inclusive

0 3239 B) 0 2639 C) 0 3305 D) 0.2914

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response.

138) Under what conditions are you allowed to use the normal distribution to approximate the binomial distribution? Under what conditions might you want to use the normal distribution to approximate the binomial as opposed to using the binomial probability formula, a table of binomial probabilities, or a computer?

138)

139) Explain why a continuity correction factor is necessary when approximating the binomial distributio n by the

normal distribution. Refer to the terms "discrete" and "continuous", and draw a diagram to support your answer.

140) According to data from the American Medical Association, 10% of us are lefthanded

Suppose a group of 500 people is randomly selected. You wish to find the probability that

at least 80 are left-handed Describe the characteristics of this problem which help you to recognize that the problem is about a binomial distribution that you are to solve by estimating with the normal distribution. (Assume that you would not use a computer, a table, or the binomial probability formula.)

141)

A fair coin is flipped 280 times. You wish to find the probability that the number of tails is greater than 160. This probability can be estimated by finding the area to the right of under the normal curve with μ = and σ = .

142)

A fair coin is flipped 360 times You wish to find the probability that the number of tails is less than 150 This probability can be estimated by finding the area that is to the left of under the normal curve with μ = and σ =

143)

A balanced die is rolled 240 times You wish to find the probability that the number of ones is at most 50 This probability can be estimated by finding the area that is to the left of under the normal curve with μ = and σ = .

144)

A balanced die is rolled 210 times You wish to find the probability that the number of fives is between 30 and 38 inclusive This probability can be estimated by finding the area between and under the normal curve with μ = and σ =

141)

142)

143)

144)

Fill in the blanks.

Fill in the blanks

Fill in the blanks.

Fill in the blanks

Answer Key

24) They are equal (at least approximately) when the area is expressed as a percentage

25) No, because the total area under the curve is 0 903, not 1

26) Both graphs will have the same shape (they will both be bell-shaped) and they will be centered at the same place (the common mean) The graph of the variable with the smaller standard deviation will be narrower and taller than the other graph

27) Responses can vary, but a correct response should resemble the following:

where

Distribution a is represented by the solid-line curve, Distribution b is represented by the dashed-line curve on the right, and Distribution c is represented by the dashed-line curve on the left.

28) B

29) Answers will vary. Possible answer: The standard normal distribution has a mean of 0 and a standard deviation of 1 while a nonstandard normal distribution can have any mean and standard deviation. It is necessary to standardize nonstandard normal distributions because a table of areas is available for the standard normal distribution but not for other normal distributions

30) Answers will vary. Possible answer: The percentage of observations between 80 and 90 is larger. Both intervals have the same length, but the interval (80, 90) is closer to the mean than the interval (120, 130).

Answer Key

Testname: UNTITLED1

31) Answers will vary. Possible answer: The area under the standard normal curve between -1 and 1 is larger. The area under the curve between 0 and 1 is common to both areas The area under the curve between -1 and 0 is larger than the area under the curve between 1 and 2 because it is closer to the mean

32) The area under the normal curve between 20 and 28 is 0.42.

33) D

34) Answers will vary Possible answer: The last step is incorrect The percentage of observations lying between 106 and 110 is not equal to the difference in the z-scores but to the area under the standard normal curve between 0 6 and 1.0. To find this area, the student would need to use a table of areas for the standard normal curve

64) A correct response should resemble the following:

65) By symmetry, the area under the standard normal curve to the left of 2 is equal to the area under the standard normal curve to the right of -2

66) By symmetry, the area under the standard normal curve to the right of 1 7 is equal to the area under the standard normal curve to the left of -1.7, which can be found by subtracting the given area from 1.

67) The area under the standard normal curve between 1 and 2 can be found by subtracting the area to the right of 2 from the area to the right of 1.

68) The area under the standard normal curve to the left of 1 can be found by subtracting the area between 1 and 3 from the area to the left of 3

69) Answers will vary. Possible answer: Find the area to the left of the z-score by subtracting 0.56 from 1 to get 0.44. Then look for the area closest to 0.44 in the body of the table and read off the corresponding z-score. (This method assumes that the students are using a table of areas that gives the area to the left of a given z-score)

70) Answers will vary Possible answer: The student's reasoning was not correct The original area should be subtracted from 1 to find the area to the left of the z-score, which is 0.48. The student should then look for the closest area to 0.48 in the body of the table and read off the corresponding z-score, which is -0.05.

97) B 98) B 99) B

100) D

101) B

102) Answers will vary Possible answer: Sketch a normal curve and shade the area associated with the given percentage

Use a table of areas for the standard normal curve to find the z-score delimiting the shaded area Find the xvalue corresponding to the z-score by using x = μ + σz

103) Answers will vary Areas under the standard normal curve must lie between 0 and 1; z-scores can take any value, positive or negative

104) A

105) B

106) A

107) A

108) Answers will vary Possible answer: In A, a percentage is given and the corresponding observation is required

The table of areas would be used to find the z-score having an area of 0 9 to its left and the z-score would then be converted to an x-value

In B, the probability that X falls in a specified range is required The x-value would be converted to a z-score and the table of areas would be used to find the area corresponding to the z-score

109) Answers will vary. Possible answer: You would look for 0.7 in the body of the table since it represents a percentage (an area), not a z-score

110)

115) Since the normal probability plot is roughly linear, it appears that scores on this test are approximately normally distributed.

116) Since the normal probability plot displays curvature, it appears that lifetimes of these batteries are probably not normally distributed

117) Since the normal probability plot is roughly linear, it appears that scores on this test are approximately normally distributed

118) Since the normal probability plot displays curvature, it appears that incomes of engineers in this town are probably not normally distributed

119) Since there are no points that fall outside the overall pattern of the plot, there are no outliers

120) Since there are no points that fall outside the overall pattern of the plot, there are no outliers

121) The point (100, 1 5) appears to be an outlier since it falls outside the overall pattern of the plot

122) The point (1350, 1.5) appears to be an outlier since it falls outside the overall pattern of the plot.

123) The rule should be interpreted more strictly for large data sets. A set of data for a normally distributed variable becomes more clearly normal the larger the set. So, for large data sets, even a small deviation from normality indicates that the variable is probably not normally distributed.

124) Because it is easier to recognize a straight line than it is to recognize the shape of a bell curve

125) Because it is especially difficult to assess the shape of a histogram when the data set is small but it is relatively easy to judge whether a string of data points forms a straight line regardless of how many points you have (as long as you have at least three or so)

126) The convention of the text is to use the vertical axis for the normal scores, but some statistical software packages and texts use the horizontal axis.

127) No. It might be that you can explain why the outlier is there, in which case you can interpret the rest of the data separate from the outlier.

138) One may use the normal distribution to approximate the binomial distribution, provided that both np and n(1p) are greater than or equal to 5. You would choose to approximate by the normal distribution if a computer and software were not available, if the table did not contain the required values of n and p, or if the computations could not be easily and expediently done with the binomial probability formula.

139) A continuity correction factor is needed because a discrete distribution is being approximated with a continuous distribution. The binomial distribution is a discrete distribution with a probability histogram made up of bars. The probability that X takes any given whole-number value is the area of the bar above the number. In the case of X = 6, for example, the probability that X = 6 is the area of the bar above 6, which runs from 5 5 to 6 5 So the area under the appropriate normal curve from 5 5 to 6 5 would approximate the area of the bar.

140) For each person, there are two possible outcomes, left-handed ("success") or right-handed ("failure"). The probability of success is the same for each person (0 10), the number of trials is fixed (500), and the trials are independent of each other. Thus the conditions for a binomial distribution are satisfied Since the number of trials is large, it would take too long to solve the problem by using the binomial formula This suggests that a normal approximation should be used

141) 160.5, 140, 8.37

142) 149.5, 180, 9.49

143) 50 5, 40, 5 77

144) 29 5, 38 5, 35, 5 40