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Solved: The Empirical Rule The following data represent

Fundamentals of Statistics | 4th Edition | ISBN: 9780321838704 | Authors: Michael Sullivan,III ISBN: 9780321838704 30

Solution for problem 23AYU Chapter 3.2

Fundamentals of Statistics | 4th Edition

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Fundamentals of Statistics | 4th Edition | ISBN: 9780321838704 | Authors: Michael Sullivan,III

Fundamentals of Statistics | 4th Edition

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Problem 23AYU

The Empirical Rule The following data represent the weights (in grams) of a random sample of 50 M&M plain candies.

(a) Determine the sample standard deviation weight. Express your answer rounded to three decimal places.

(b) On the basis of the histogram drawn in Section 3.1, Problem 27, comment on the appropriateness of using the Empirical Rule to make any general statements about the weights of M&Ms.

(c) Use the Empirical Rule to determine the percentage of M&Ms with weights between 0.803 and 0.947 gram.

(d) Determine the actual percentage of M&Ms that weigh between 0.803 and 0.947 gram, inclusive.

(e) Use the Empirical Rule to determine the percentage of M&Ms with weights more than 0.911 gram.

(f) Determine the actual percentage of M&Ms that weigh more than 0.911 gram.

Step-by-Step Solution:

Step 1 of 2

a)

First we need to find mean.

 = 

 = 

 = 0.766

Here standard deviation is

 = 

 = 0.0012

Then the sample variance is

s =

s =

s = 0.036

Hence the sample variance is s = 0.036 gram.

Step 2 of 2

Chapter 3.2, Problem 23AYU is Solved
Textbook: Fundamentals of Statistics
Edition: 4
Author: Michael Sullivan,III
ISBN: 9780321838704

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Solved: The Empirical Rule The following data represent