Introduction to Probability and Statistics
Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
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Textbook Question
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Chapter 2, Problem 2.54SE

Raisins The number of raisins in each of 14miniboxes (1/2 -ounce size) was counted for ageneric brand and for Sunmaid brand raisins. Thetwo data sets are shown here:
Chapter 2, Problem 2.54SE, Raisins The number of raisins in each of 14miniboxes (1/2 -ounce size) was counted for ageneric

a. What are the mean and the standard deviation for thegeneric brand?
b. What are the mean and the standard deviation for theSunmaid brand?
c. Compare the centers and variabilities of the twobrands using the results of parts a and b.

Expert Solution
Check Mark
To determine

(a)

To find:

The mean and standard deviation for the generic brand.

Answer to Problem 2.54SE

The mean and standard deviation for the generic brand are 26.21 and 1.2514 respectively.

Explanation of Solution

Given information:

The given data is,

Generic Brand Sunmaid
25 26252825292424
2628282728242822
2627242525283027
26 26 2824

Calculation:

The data with calculation is shown in table below.

x(xx¯)2
251.464 1
260.044 1
260.044 1
260.044 1
260.044 1
283.204 1
270.624 1
260.044 1
251.464 1
283.204 1
244.884 1
283.204 1
270.624 1
251.464 1
Total36720.3574

  Table-1

The sample size is n=14.

The mean is,

  x¯=xn=36714=26.21

The standard deviation is,

  s= ( x x ¯ ) 2 n1= 20.3574 141=1.2514

Therefore, the mean and standard deviation for the generic brand are 26.21 and 1.2514 respectively.

Expert Solution
Check Mark
To determine

(b)

To find:

The mean and standard deviation for Sunmaid.

Answer to Problem 2.54SE

The mean and standard deviation for the generic brand are 26.14 and 2.4133 respectively.

Explanation of Solution

Given information:

The given data is,

Generic Brand Sunmaid
25 26252825292424
2628282728242822
2627242525283027
26 26 2824

Calculation:

The data with calculation is shown in table below.

x(xx¯)2
251.2996
283.4596
251.2996
283.4596
298.1796
244.5796
283.4596
244.5796
244.5796
283.4596
3014.8996
244.5796
2217.1396
270.7396
Total36675.7144

  Table-2

The sample size is n=14.

The mean is,

  x¯=xn=36614=26.14

The standard deviation is,

  s= ( x x ¯ ) 2 n1= 75.7144 141=2.4133

Therefore, the mean and standard deviation for the generic brand are 26.14 and 2.4133 respectively.

Expert Solution
Check Mark
To determine

(c)

To compare:

The centers and variability of the brands.

Explanation of Solution

Given information:

The given data is,

Generic Brand Sunmaid
25 26252825292424
2628282728242822
2627242525283027
26 26 2824

The generic brand has smaller standard of deviation as compared to Sunmaid and the mean of generic brand is greater as compared to Sunmaid.

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Chapter 2 Solutions

Introduction to Probability and Statistics

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