## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 6 - Normal Probability Distributions - 6-5 The Central Limit Theorem - Basic Skills and Concepts - Page 293: 13

#### Answer

a. $0.9787$ b. $21.08$ to $24.22$ c. $0.9998$; No

#### Work Step by Step

a) We first find the two $z$-scores: $z=\frac{25−22.65}{0.8}=2.94$ $z=\frac{21−22.65}{0.8}=−2.06$ Using the table of z-scores, we find: $0.9984−0.0197=0.9787$ b) Using the table of negative $z$-scores, we can find that this corresponds to a value of $z=±1.96$. Hence: $max=22.65+(0.8)(1.96)=24.22$ $min=22.65+(0.8)(−1.96)=21.08$ c) Using $z$-scores, we can find that the probability is $0.9998$. However, because this represents the mean of women and not the general population, it does not follow that the majority of women will be able to fit in these hats.

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