Solution Manual for Applied Statistics and Probability for Engineers 7th by Montgomery Visit to download the full and correct content document: https://testbankbell.com/dow nload/solution-manual-for-applied-statistics-and-probability-for-engineers-7th-by-mont gomery/
Solution Manual for Applied Statistics and Probability for Engineers
7th by Montgomery
To download the complete and accurate content document, go to: https://testbankbell.com/download/solution-manual-for-applied-statistics-and-probabili ty-for-engineers-7th-by-montgomery/
CHAPTER 6
Section 6.1
6.1.1 No, usually not For example, if the sample is {2, 3} the mean is 2.5 which is not an observation in the sample.
6.1.7 Sample average:
The sample standard deviation could also be found using
Applied Statistics and Probability for Engineers, 7th edition 6-1
43.975 8 351.8 = = x Sample variance: ( ) 151.143 7 998 1057 1 8 8 8 351 16528.043 1 16528403 351.8 2 2 1 1 2 2 19 1 2 8 1 = = = = = = = = = = n n x x s x x n i i n i i i i i i Sample standard deviation: 12.294 151.143 = = s
( ) 1 1 2 = = n x x s n i i where ( ) 1057.998 8 1 2 = =i i x x Dot Diagram: . . .. . .. . + + + + + + 24.0 32.0 40.0 48.0 56.0 64.0 Solution Manual for Applied Statistics and Probability for Engineers 7th by Montgomery Visit TestBankBell.com to get complete for all chapters
6.1.8
6.1.9
Applied Statistics and Probability for Engineers, 7th edition 6-2
Sample average: mm n x x n i i 173 2 9 19.56 1 = = = = Sample variance: ( ) 2 2 2 1 1 2 2 9 1 2 9 1 ) ( 0.4303 8 3.443 1 9 9 19.56 953 45 1 953 45 19.56 mm n n x x s x x n i i n i i i i i i = = = = = = = = = = Sample standard deviation: mm s 6560 0 4303 0 = =
. . . . . . . .. + + + + + crack length 1.40 1.75 2.10 2.45 2.80 3.15
Dot Diagram
Sample average of exercise group: 287.89 12 3454.68 1 = = = = n x x n i i Sample variance of exercise group: 1 12 12 (3454.68) 1118521.54 1 s 1118521.54 3454.68 2 2 1 1 2 2 1 2 1 = = = = = = = = n n x x x x n i i n i i n i i n i i
Dot Diagram of no exercise group:
Applied Statistics and Probability for Engineers, 7th edition 6-3 11268.52 11 123953.71 = =
standard deviation of exercise group: 106.15 11268.52 = = s
Diagram of exercise group: Sample average of no exercise group: 325.010 8 2600.08 1 = = = = n x x n i i Sample variance of no exercise group: 1 8 8 (2600.08) 947873.4 1 s 947873.4 2600.08 2 2 1 1 2 2 1 2 1 = = = = = = = = n n x x x x n i i n i i n i i n i i 14688.77 7 102821.4 = = Sample standard deviation of no exercise group: 121.20 14688.77 = = s
Sample
Dot
No Exercise 500 450 400 350 300 250 200 150 Dotplot of No Exercise
6.1.10 Dot Diagram of CRT data (Data were rounded for the plot)
The data are distributed at lower values in the second experiment. The lower CRT resolution reduces the visual accommodation.
6.1.11 a) 65.86 = x
6.1.12
b) Removing the smallest observation (31), the sample mean and standard deviation becomes 66.86 = x
10.74 F
a) All 52
Applied Statistics and Probability for Engineers, 7th edition 6-4
Dot Diagram : : . . . . .. .: .: . .:..: .. :: .... .. -+ + + + + + temp 30 40 50 60 70 80
F 12.16 = s F
F s =
Sample mean: 303.2865 52 15770.9 1 = = = = n x x n i i Sample variance: ( ) 265224.8 51 13526462 1 52 52 15770.9 18309564 1 18309564 15770.9 2 2 1 1 2 2 52 1 2 52 1 = = = = = = = = = = n n x x s x x n i i n i i i i i i Sample standard deviation: 64 56 48 40 32 24 16 8 Accomodation1 Accomodation2 Data DotplotofAccomodation1,Accomodation2
clouds:
Applied Statistics and Probability for Engineers, 7th edition 6-5 514.9998 265224.8 = = s Range: Maximum= 2745.6, Minimum= 1, Range= 2745.6 - 1 = 2744.6 b) Unseeded Clouds: Sample mean: 588 164 26 4279.3 1 = = = = n x x n i i Sample variance: ( ) 77521.26 25 1938032 1 26 26 4279.3 2642355 1 2642355 4279.3 2 2 1 1 2 2 26 1 2 26 1 = = = = = = = = = = n n x x s x x n i i n i i i i i i Sample standard deviation: 278.4264 77521.26 = = s Range: Maximum= 1202.6, Minimum= 1, Range= 1202.6-1 = 1201.6 c) Seeded Clouds: Sample mean: 441.985 26 11491.6 1 = = = = n x x n i i Sample variance: ( ) 423524 25 10588099 1 26 26 11491.6 15667208.96 1 15667208.96 11491.6 2 2 1 1 2 2 26 1 2 26 1 = = = = = = = = = = n n x x s x x n i i n i i i i i i Sample standard deviation: 650.787 423524 = = s
Range:
Maximum= 2745.6, Minimum= 4.1, Range= 2745.6-4.1 = 2741.5
6.1.13 Dot Diagram for Unseeded clouds:
Dot Diagram for Seeded clouds:
The sample mean for unseeded clouds is 164.588 and the data is not centered about the mean. Two large observations increase the mean. The sample mean for seeded clouds is 441.985 and the data is not centered about the mean. The average rainfall when clouds are seeded is higher when compared to the rainfall when clouds are not seeded. The amount of rainfall for seeded clouds varies more widely than the amount of rainfall for unseeded clouds.
6.1.14 Sample mean:
Applied Statistics and Probability for Engineers, 7th edition 6-6
52.6476 71 3737.98 1 = = = = n x x n i i Sample variance: ( ) 58.614 70 4102.98 1 71 71 98 3737 200899 1 200899 3737.98 2 2 1 1 2 2 71 1 2 71 1 = = = = = = = = = = n n x x s x x n i i n i i i i i i Sample standard deviation: 7.65598 58.614 = = s
Dot Diagram:
There appears to be an outlier in the data.
Section 6.2
6.2.1 A back-to-back steam-and-leaf display is useful when two data sets are to be compared
How does the back-to-back stem-and-leaf display show the differences in the data set in a way that the dotplot cannot? The back-to-back stem-and-leaf display more easily compares the minimum and maximum values, the distribution of the data, and possibly the median and mode(s).
6.2.2 The median will be equal to the mean when the sample is symmetric about the mean value.
6.2.3 The median will equal the mode when the sample is symmetric with a single mode. The symmetry implies the mode is at the median of the sample.
6.2.4
6.2.5
Applied Statistics and Probability for Engineers, 7th edition 6-7
Stem-and-leaf of C1 N = 82 Leaf Unit = 0.10 1 83 4 3 84 33 4 85 3 7 86 777 13 87 456789 24 88 23334556679 34 89 0233678899 (13) 90 0111344456789 35 91 0001112256688 22 92 22236777 14 93 023347 8 94 2247 4 95 4 96 15 2 97 2 98 8 1 99 1 100 3 Q1 Median Q3 88.575 90.400 92.200
Stem-and-leaf display
to failure: unit = 100 1|2 represents 1200 1 0T|3 1 0F| 5 0S|7777 10 0o|88899
for cycles
22 1*|000000011111
33 1T|22222223333
(15) 1F|444445555555555
22 1S|66667777777
11 1o|888899
5 2*|011
2 2T|22
Median = 1436.5, Q1 = 1097.8, and Q3 = 1735.0
No, only 5 out of 70 coupons survived beyond 2000 cycles.
6.2.6 The data in the 42nd is 90.4 which is median.
The mode is the most frequently occurring data value. There are several data values that occur 3 times. These are: 86.7, 88.3, 90.1, 90.4, 91, 91.1, 91.2, 92.2, and 92.7, so this data set has a multimodal distribution.
6.2.7 Sample median is at
= 35.5th observation, the median is 1436.5.
Modes are 1102, 1315, and 1750 which are the most frequent data.
6.2.8 Sample mean: 65.811 = x inches, standard deviation 2.106 = s inches, and sample median: 66.000 ~ = x inches
Stem-and-leaf display of female engineering student heights N = 37 Leaf
represents 61.0 inches
6.2.9 Stem-and-leaf display Strength: unit = 1.0 1|2
Applied Statistics and Probability for Engineers, 7th edition 6-8
Sample mean: 90.534 83 7514.3 1 = = = = n x x n i i
( ) 2 1 70 +
Sample mean: 1403.7 70 98259 1 = = = = n x x n i i
Unit = 0.10
1 61|0 3 62|00 5 63|00 9 64|0000 17 65|00000000 (4) 66|0000 16 67|00000000 8 68|00000 3 69|00 1 70|0
61|0
represents 12 1 532|9
1 533|
2 534|2
4 535|47
5 536|6
9 537|5678
20 538|12345778888
26 539|016999
37 540|11166677889
46 541|123666688
(13) 542|0011222357899
41 543|01111556
33 544|00012455678
22 545|233447899
13 546|23569
8 547|357
5 548|11257
6.2.10 Stem-and-leaf of concentration, N = 60, Leaf Unit = 1.0, 2|9 represents 29 Note: Minitab has dropped the value to the right of the decimal to make this display.
1 2|9
2 3|1
3 3|9
8 4|22223
12 4|5689
20 5|01223444
(13) 5|5666777899999
27 6|11244
22 6|556677789
13 7|022333
7 7|6777
3 8|01
8|9
The data have a symmetrical bell-shaped distribution, and therefore may be normally distributed.
Applied Statistics and Probability for Engineers, 7th edition 6-9
5480.8 95 95.5 95 100 100 0.5 is percentile i i th = =
1
Sample Mean 59.87 60 3592.0 1 = = = = n x x n i i Sample Standard Deviation ( ) 50 12 20 156 and 156.20 59 9215.93 1 60 60 0 3592 224257 1 224257 and 0 3592 2 2 1 1 2 2 60 1 2 60 1 = = = = = = = = = = = = s n n x x s x x n i i n i i i i i i Sample Median 59.45 ~ = x
6.2.12
22/40
of the taste testers considered this particular Pinot Noir truly exceptional.
Applied Statistics and Probability for Engineers, 7th edition 6-10 Variable N Median concentration 60 59.45 76.85 90 54.5 90 100 60 0.5 is percentile i i th = = 6.2.11 Stem-and-leaf display. Rating: unit = 01.0 1|2 represents 12 1 8|3 2 8|4 5 8|555 7 8|66 9 8|77 12 8|888 18 8|999999 (7) 9|0000000 15 9|1111111 8 9|2222 4 9|3 3 9|4 2 9|55 Sample Mean 89.45 40 3578 40 40 1 1 = = = = = = i i n i i x n x x Sample Standard Deviation ( ) 2.8 8.05 and 05 8 39 9 313 1 40 40 3578 320366 1 320366 and 3578 2 2 1 1 2 2 40 1 2 40 1 = = = = = = = = = = = = s n n x x s x x n i i n i i i i i i Sample Median Variable N Median rating 40 90.000
= 55%
Stem-and-leaf diagram of NbOCl3 N
27 Leaf Unit = 100 0|4 represents 40 gram-mole/liter x 10-3
=
The male engineering students are taller than the female engineering students. Section
Applied Statistics and Probability for Engineers, 7th edition 6-11 6 0|444444 7 0|5 (9) 1|001122233 11 1|5679 7 2| 7 2|5677 3 3|124 Sample mean 3 27 1 mole/literx10 gram 1539 27 41553 27 = = = = i ix x Sample Standard Deviation ( ) -3 2 2 1 1 2 2 27 1 2 27 1 -mole/literx10 gram 62 957 91703085 and 91703085 26 23842802 1 27 27 41553 87792869 1 87792869 and 41553 = = = = = = = = = = s n n x x s x x n i i n i i i i i i Sample Median 3 mole/literx10 gram 1256 ~ = x Variable N Median NbOCl3 40 1256 6.2.13 Stem-and-leaf display. Height: unit = 0.10 1|2 represents 1.2 Female Students| Male Students 0|61 1 00|62 3 00|63 5 0000|64 9 00000000|65 17 2 65|00 0000|66 (4) 3 66|0 00000000|67 16 7 67|0000 00000|68 8 17 68|0000000000 00|69 3 (15) 69|000000000000000 0|70 1 18 70|0000000 11 71|00000 6 72|00 4 73|00 2 74|0 1 75|0
6.3 6.3.1 Frequency Tabulation for Exercise 6.2.5 - Cycles to Failure
6.3.2
Solution uses the n = 83 observations from the data set. Frequency Tabulation for Exercise 6.2.4.Octane Data
Applied Statistics and Probability for Engineers, 7th edition 6-12 Lower Upper Relative Cumulative Cum. Rel. Class Limit Limit Midpoint Frequency Frequency Frequency Frequency at or below .000 0 .0000 0 .0000 1 .000 266.667 133.333 0 .0000 0 .0000 2 266.667 533.333 400.000 1 .0143 1 .0143 3 533.333 800.000 666.667 4 .0571 5 .0714 4 800.000 1066.667 933.333 11 .1571 16 .2286 5 1066.667 1333.333 1200.000 17 .2429 33 .4714 6 1333.333 1600.000 1466.667 15 .2143 48 .6857 7 1600.000 1866.667 1733.333 12 .1714 60 .8571 8 1866.667 2133.333 2000.000 8 .1143 68 .9714 9 2133.333 2400.000 2266.667 2 .0286 70 1.0000 above 2400.000 0 .0000 70 1.0000 Mean = 1403.66 Standard Deviation = 402.385 Median = 1436.5
Lower Upper Relative Cumulative Cum. Rel. Class Limit Limit Midpoint Frequency Frequency Frequency Frequency at or below 81.75 0 .0000 0 .0000 1 81.75 84.25 83.0 1 .0120 1 .0120 2 84.25 86.75 85.5 6 .0723 7 .0843 3 86.75 89.25 88.0 19 .2289 26 .3133 4 89.25 91.75 90.5 33 .3976 59 .7108 5 91.75 94.25 93.0 18 .2169 77 .9277 6 94.25 96.75 95.5 4 .0482 81 .9759 7 96.75 99.25 98.0 1 .0120 82 .9880 8 99.25 101.75 100.5 1 .0120 83 1.0000 above 101.75 0 .0000 83 1.0000 2250 2000 1750 1500 1250 1000 750 500 15 10 5 0 number of cycles to failure F r e q u e n c y
Histogram 8 bins:
Histogram 16 bins:
HistogramofCyclestofailure(8bins)
Applied Statistics and Probability for Engineers, 7th edition 6-13 Mean = 90.534 Standard Deviation = 2.888 Median = 90.400
6.3.3
100 5 98 0 95 5 93 0 90 5 88 0 85 5 83 0 30 20 10 0 octane data F r e q u e n c y Cyclestofailureofaluminumtestcoupons F r e q u e n c y 2250 2000 1750 1500 1250 1000 750 500 18 16 14 12 10 8 6 4 2 0
