Solution Manual for Elementary Statistics A Step by Step Approach
9th Edition by Bluman
ISBN 1259199703 9781259199707
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) Identifythe type of distribution pattern that occurs when the majorityof the data values fall to the left of the mean?
A) symmetrical
C) positivelyskewed
B) left skewed
D) negativelyskewed
2) When the majorityof the data values fall to the right of the mean, the distribution is said to be left-skewed.
A) True
2)
B) False
3) The figure below is an example of a negativelyskewed distribution.
3)
A) True
B) False
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
4) When the data values are evenlydistributed about the mean, the distribution is said to be .
4)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
5) Which choice is another term that can be used to describe a normal distribution:

A) discrete distribution
C) negativelyor positivelyskewed
B) bell curve
D) independent variable
6) On an easytest, the mean score was 96 out of a possible 100 points The distribution of the test scores is likelyto be
A) diagonallyskewed.
C) positivelyskewed.
B) symmetric
D) negativelyskewed.
7) Which of the following characteristics does not applyto a theoretical normal distribution?
A) It is bimodal.
5)
6)
It is never negative.
C) The mean, median, and mode are equal.
D) It is bell-shaped.
8) In applied statistics, it is the area under the normal distribution curve which is most important, not the value of single points on the curve.
A) True B) False
9) The normal distribution curve can be used as a probabilitydistribution curve for normally distributed variables
A) True B) False
10) If a normal distribution has a mean of 35 and a standard deviation of10, then
A) the median is 45 and the mode is 25. B) the median is 35 and the mode is 45.
C) the median is 25 and the mode is 45. D) the median is 35 and the mode is 35.
11) For a normal distribution curve with a mean of 15 and a standard deviation of 5, which range of the variable defines an area under the curve corresponding to a probabilityof approximately68%?
A) from 12 5 to 17 5
C) from 5 to 25
9)
10)
11)
B) from 10 to 20
D) from 15 to 25
12) One normal curve has a mean of24 and a standard deviation of3. A second normal curve has a mean of 3 and a standard deviation of 24. The curve that is more dispersed, or spread out, is
A) both; theyare equallyspread out.
B) the first normal curve
C) the second normal curve.
D) neither; bydefinition,a normal curve shows no spread.
13) For a normal distribution curve with a mean of 9 and a standard deviation of 5, which of the following ranges of the variable will define an area under the curve corresponding to a probabilityof approximately34%?
A) from 4 to 14
C) from -1 to 19
12)
13)
B) from 6.5 to 11.5
D) from 9 to 14
14) Which of the following properties distinguishes the standard normal distribution from other normal distributions?
A) The total area under the curve is equal to 1 00.
B) The mean is 0 and the standard deviation is 1.
C) The curve is continuous.
D) The mean is located at the center of the distribution.
14)
15) The number of standard deviations a particular X value is from the mean is commonly 15)
referred to as .
A) P(X) B) z C) σ 2 D) μ
16) The area under the normal distribution curve that lies within three standard deviations of the mean is approximately95%.
A) False B) True
17) To find the area under the standard normal distribution curve between two z values, one first finds the difference between the two z values, then locates the value corresponding to that difference in the Standard Normal Distribution table.
A) True B) False
18) The area under a normal distribution curve is always positive even if the z value is negative.

A) True B) False
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
19) Stating that the area under the standard normal distribution curve between z = 0 and z = 1.00 is 0.3413, is the same as stating that the of randomly selecting a standard normallydistributed variable z with a value between 0 and 1.00 is 0.3413.
19)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
20) Find the area under the standard normal distribution curve between z = 0 and z = 2.16.
21) Find the area under the standard normal distribution curve between z = 0 and z = -2
22) The area under the standard normal distribution curve to the right of z = 1 83 is 0 4664.



23) What is the area under the standard normal distribution curve between z = 1.50 and z
2 50?
24) Find the area under the standard normal distribution curve between z = –2.05 and z = 2 05.

36) Find the probability P(z > -0 54) using the standard normal distribution
37) Find the probability P(z < 0.37) using the standard normal distribution.



38) Find the z value that corresponds to the given area
39) Find the z value that corresponds to the given area.
40) Find the z value that corresponds to the given area.
41) Find the z-score for which the area to the left is 0 13
42) Find the z-score for which the area to the right is 0.27.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question
43) Find the z value to the right of the mean so that 62.93% of the area under the distribution curve lies to the left of it.
44) Find the z value to the right of the mean such that 85% of the total area under the standard normal distribution curve lies to the left of it?
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 45) Find the z-scores that bound the middle 74% of the area under the standard normal curve.
46) Find the probability P(-0.72 < z < -0.11) using the standard normal distribution.
47) In a standard normal distribution, what z value corresponds to 17% of the data between the mean and the z value?

48) If a normallydistributed group of test scores have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below 50.
49) A normal population has a mean μ = 28 and standard deviation σ = 5. What proportion of the population is less than 23?
50) A normal population has a mean μ = 33 and standard deviation σ = 9. What is the probabilitythat a randomlychosen value will be greater than 44?
0.8554
51) A normal population has a mean μ = 40 and standard deviation σ = 11. What proportion of the population is between 24 and 32?
52) A bottler of drinking water fills plastic bottles with a mean volume of 998 milliliters (mL) and standard deviation 7 mL. The fill volumes are normally distributed. What proportion of bottles have volumes greater than 999 mL?
53) A bottler of drinking water fills plastic bottles with a mean volume of 1001 milliliters (mL) and standard deviation 6 mL. The fill volumes are normallydistributed. What proportionof bottles have volumes less than1001 mL?
54) A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (mL) and standard deviation 5 mL The fill volumes are normally distributed. What proportion of bottles have volumes between 992 mL and 998 mL?
55) The weights of 6-week-old poults (juvenile turkeys) are normallydistributed with a mean 8.9 pounds and standard deviation 1.9 pounds. A turkeyfarmer wants to provide a money-back guarantee that her 6-week poults will weigh at least a certain amount. What weight should she guarantee so that she will have to give her customer's moneyback only 1% of the time? A) 4.47 lb
4.02 lb
56) The average length of crocodiles in a swamp is 11 5 feet If the lengths are normally distributed with a standard deviation of 1 7 feet, find the probabilitythat a crocodile is more than 11 feet long. A) 0 62
57) At a large department store, the average number of years of employment for a cashier is 5 7 with a standard deviation of 1 8 years, and the distribution is approximatelynormal If an employee is picked at random, what is the probabilitythat the employee has worked at the store for over 10 years? A) 1 7% B) 49 2%
58) The average hourlywage of workers at a fast food restaurant is $6.50/hr. Assume the wages are normallydistributed with a standard deviation of $0.45. If a worker at this fast food restaurant is selected at random, what is the probabilitythat the worker earns more than $6 75?
A) 42 1% B) 27 6%
59) The average gas mileage of a certain model car is 30.0 miles per gallon. If the gas mileages are normallydistributed with a standard deviation of 0 75 miles per gallon, find the probabilitythat a car has a gas mileage of between 29 8 and 30 2 miles per gallon
A) 0 213 B) 0 273
60) The average height of flowering cherrytrees in a certain nurseryis 10.5 feet. If the heights are normallydistributed with a standard deviation of1.5 feet, find the probability that a tree is less than 12 5 feet tall
A) 0 96 B) 0 73
0 82
61) A recent studyfound that the life expectancyof a people living in Africa is normally distributed with an average of 53 years with a standard deviation of 7 5 years If a person in Africa is selected at random, what is the probabilitythat the person will die before the age of 65?
A) 89.0%
44.5%
62) X is a normallydistributed random variable with a mean of 7.0 and a standard deviation of 3 00 Find the value x such that P(X < x) is equal to 0 86. (Note: the diagram is not necessarilyto scale.)

63) X is a normallydistributed random variable with a mean of 11 00. If the probabilitythat X is less than 11 88 is 0 67 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarilyto scale.)
64) In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualifyfor acceptance into the university? A) 1400 B) 1250
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
65) Mrs Smith's reading class can read an average of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. What is the minimumnumber of words per minute a student would need to read in order to get the award? Assume the data is normally distributed.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
66) X is a normallydistributed random variable with a mean of4.0. Find the standard deviation of the distribution if 59.10% of the data lies to the right of 3.54. (Note: the diagram is not necessarilyto scale.)


67) X is a normallydistributed random variable with a mean of10 and a standard deviation of 4 0 Find the value of X for which 70 54% of the area under the distribution curve lies to the right of it (Note: the diagram is not necessarilyto scale )
68) X is a normallydistributed random variable with a standard deviation of 3.50. Find the mean of X when 64.8% of the area lies to the left of 5.33. (Note: the diagram is not necessarilyto scale.)
69) X is a normallydistributed random variable with a standard deviation of 2.00. Find the mean of X if 12.71% of the area under the distribution curve lies to the right of 10.28. (Note: the diagram is not necessarilyto scale.)



70) The data shown represent quiz scores from Ms. Mayer's 5th grade class. Use the Pearson coefficient to check for skewness.
21 25 9 21 23 22 22 15 23 22 16 11 20 20 17 22 21
A) | PC | < 1 so data is skewed
C) | PC | > 1 so data is skewed
B) | PC | < 1 so data is not skewed
D) | PC | > 0 so data is skewed
71) For a normal distribution with a mean of 7 and a standard deviation of 6, the value 10 has a z value of
72) For a normal distribution with a mean of 13 and a standard deviation of 6, the value 1 has a z value of
73) The following formula can be used to find the specific value of the variable in a data set that corresponds to a particular value of the standard normal variable:
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
74) What is the z value such that 50% of the total area under the standard normal distribution curved lies to the right of it?
75) A(n) is a distribution of means obtained from samples of a specific size taken from a population
MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question 76) The difference between a sample mean and the population mean maybe referred to as . A) sampling error B) the standard deviation C) the variance D)
77) If the standard deviation of a normallydistributed population is 55.0 and we take a sample of size 25, then the standard error of the mean is
78) In order to have the standard error of the mean be 15, one would need to take samples from a normallydistributed population with a standard deviation of 78)
79) The standard deviation of sample means will be larger than the standard deviation of the population.
A) False B) True
79)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 80) The correction factor is important if a relativelylarge number of samples are taken without replacement from a small population 80)
81) As the sample size n increases, the shape of the distribution of the sample means taken with replacement from a population with mean μ and standard deviation σ, will approach a normal distribution This distribution will have a mean of μ and a
standard deviation of σ n This is a statement of the
82) The standard deviation of a normal distribution is 20. What is the standard error of the mean obtained byaveraging 225 samples?
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 83) A sample of size 65 will be drawn from a population with mean 22 and standard deviation15. Find the probabilitythat x will be between20 and 25.
84) A sample of size 50 will be drawn from a population with mean 76 and standard deviation14. Find the 69th percentile of x
85) A sample of size 45 will be drawn from a population with mean 10 and standard deviation5. Find the probabilitythat x will be greater than 11.
86) A sample of size 52 will be drawn from a population with mean 18 and standard deviation13. Find the probabilitythat x will be less than 21.
87) A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza deliverycompanybuys 43 of these cars. What is the probability that the average mileage of the fleet is greater than 33 5 mpg?
88) A certain car model has a mean gas mileage of 28 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza deliverycompanybuys 37 of these cars. What is the probability that the average mileage of the fleet is between27.2 and 28.8 mpg?
89) The mean number of pets per household is 2.96 with standard deviation 1.4. A sample of 52 households is drawn. Find the 74thpercentile of the sample mean.
90) A ferrywill safelyaccommodate 91 tons of passenger cars. Assume that the mean weight of a passenger car is 2.1 tons with standard deviation 0.7 tons. If a random sample of 40 cars are loaded onto the ferry, what is the probabilitythat the maximumsafe weight will be exceeded?
91) The mean annual income for people in a certain city (in thousands of dollars) is 43, with a standard deviation of 29. A pollster draws a sample of 41 people to interview. What is the probabilitythat the sample mean income is less than42 (thousands of dollars)?
92) The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 34. A pollster draws a sample of 58 people to interview. What is the probabilitythat the sample mean income is between 38 and 44 (thousands of dollars)?
93) The average age of vehicles registered in the United States is 96 months Assume the population is normallydistributed with a standard deviation of 15 months Find the probabilitythat the mean age of a sample of 36 vehicles is between 98 and 100 months?
94) The average age of doctors in a certain hospital is 45 0 years old. Suppose the distribution of ages is normal and has a standard deviation of8 0 years If 9 doctors are chosen at random for a committee, find the probabilitythat the average age of those doctors is less than 46 9 years Assume that the variable is normallydistributed. A) 75 8% B) 59 8%
25 8%
24 2%
95) The mean weight of loads of rock is 51 0 tons with a standard deviation of10 0 tons If 36 loads are chosen at random for a weight check, find the probabilitythat the mean weight of those loads is less than50.3 tons. Assume that the variable is normally distributed.
A) 84.09 B) 15.91
65.91
34.09
96) The average number of mosquitos in a stagnant pond is 80 per square meter with a standard deviation of 12. If 36 square meters are chosen at random for a mosquito count, find the probabilitythat the average of those counts is more than 81 8 mosquitos per square meter Assume that the variable is normallydistributed.
A) 0.3% B) 31.6% C) 81.6% D) 18.4%
97) The length of countryand western songs is normallydistributed and has a mean of190 seconds and a standard deviation of30 seconds Find the probabilitythat a random selection of16 songs will have mean length of 181 98 seconds or less Assume the distribution of the lengths of the songs is normal
A) 0 64 B) 0 14 C) 0 36 D) 0 86
98) The average diameter of sand dollars on a certain island is 3.00 centimeters with a standard deviation of 1 00 centimeters If 9 sand dollars are chosen at random for a collection, find the probabilitythat the average diameter of those sand dollars is more than2.60 centimeters. Assume that the variable is normallydistributed.
A) 0.820 B) 0.385 C) 0.885 D) 0.615
97)
98)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
99) A surveyof 250 lobster fishermen found that theycatch an average of 32.0 pounds of lobster per day with a standard deviation of 4.0 pounds. If a random sample of 36 lobster fishermen is selected, what is the probabilitythat their average catch is less than 31.5 pounds? Assume the distribution of the weights of lobster is normal.
99)
100) A(n) is employed when a continuous distribution is used to approximate a discrete distribution. 100)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
101) Use the normal approximation to the binomial to find that probabilityfor the specific value of X
n = 30, p = 0.4, X = 5
A) 0.17 B) 0.4 C) 0.07 D) 0.20
102) Use the normal approximation to find the indicated probability The sample size is n, the population proportionof successes is p, and X is the number of successes in the sample.
n = 78, p = 0.59: P(X > 42)
A) 0.2236 B) 0.7910 C) 0.8051 D) 0.7764
101)
102)
103) Use the normal approximation to find the indicated probability. The sample size is n, the population proportionof successes is p, and X is the number of successes in the sample. n = 77, p = 0 33: P(X ≤ 18)
104) Use the normal approximation to find the indicated probability. The sample size is n, the population proportionof successes is p, and X is the number of successes in the sample n = 90, p = 0 6: P(X ≥ 63)
105) Use the normal approximation to find the indicated probability The sample size is n, the population proportionof successes is p, and X is the number of successes in the sample.
n = 78, p = 0 75: P(X < 68)
106) Use the normal approximation to find the indicated probability The sample size is n, the population proportionof successes is p, and X is the number of successes in the sample. n = 90, p = 0 41: P(32 < X < 43)
107) Use the normal approximation to find the indicated probability The sample size is n, the population proportionof successes is p, and X is the number of successes in the sample
p = 0 52: P(34 ≤ X ≤ 47)
108) A gardener buys a package of seeds. Seventy-six percent of seeds of this type germinate. The gardener plants 110 seeds. Approximate the probabilitythat fewer than 77 seeds germinate.
109) A gardener buys a package of seeds Seventy-ninepercent of seeds of this type germinate The gardener plants 110 seeds Approximate the probabilitythat 84 or more seeds germinate
110) A gardener buys a package of seeds. Eighty-one percent of seeds of this type germinate. The gardener plants 120 seeds. Approximate the probabilitythat the number of seeds that germinate is between 89.2 and 105.2 exclusive.
0 9199
0 0401
111) Of the members of a BoyScout troop, 15% have received the first aid merit badge If 40 boyscouts are selected at random, find the probabilitythat four or more will have the first aid merit badge?
112) A biologist estimates that 70% of the deer in a region carrya certain type of tick. For a sample of 300 deer selected at random, what is the chance that 216 or fewer deer have this tick?
113) If a baseball player's batting average is 0 340 (i e , the probabilityof getting a hit each time at bat is 0 340), find the probabilitythat the player will have a bad season and get at most 60 hits in 200 times at bat?
114) A magazine reported that 6% of American drivers admit to reading the newspaper while driving. If 500 drivers are selected at random, find the probabilitythat exactly 40 will admit to reading the newspaper while driving.