how many inches is the lower bound? how many inches is the upper bound?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of

2.66

inches and a standard deviation of

0.05

inch. A random sample of

12

tennis balls is selected.

The probability is
63​%
that the sample mean will be between what two values symmetrically distributed around the population​ mean?
 
how many inches is the lower bound? how many inches is the upper bound?
​(Round to two decimal places as​ needed.)
Expert Solution
Step 1

Let , X→N(μ=2.66 , σ=0.05) , n=12

By using central limit theorem ,

The sampling distribution of the sample mean is approximately normal.

X¯N(μX¯=μ,σX¯=σn)

Our aim is to find the lower bound.

 

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