Chapter PI, Problem 5RE

(a)

To determine

To explain what does the greater standard deviation for men’s height indicate.

Explanation of Solution

In the question, it is given to join Beanstalk clubs a man must be over $6\text{'}2\text{'}\text{'}$ tall and a women over $5\text{'}10\text{'}\text{'}$ tall. The heights of adults may be normally distributed with mean heights of $69.1\text{'}\text{'}$ for men and $64\text{'}\text{'}$ for women. The respective standard deviation are $2.8\text{'}\text{'}\text{ and 2}\text{.5''}$ . Thus, the greater standard deviation for men’s height indicates that the heights of men are variable which can be in a range of plus and minus mean from the standard deviation.

(b)

To determine

To explain who are more likely to qualify for Beanstalk membership, men or women.

Answer to Problem 5RE

Men are more likely to qualify for Beanstalk membership.

Explanation of Solution

In the question, it is given to join Beanstalk clubs a man must be over $6\text{'}2\text{'}\text{'}$ tall and a women over $5\text{'}10\text{'}\text{'}$ tall. The heights of adults may be normally distributed with mean heights of $69.1\text{'}\text{'}$ for men and $64\text{'}\text{'}$ for women. The respective standard deviation are $2.8\text{'}\text{'}\text{ and 2}\text{.5''}$ . Thus, to find out who are more likely to qualify for Beanstalk membership, men or women let us first find the z -score as:

  $\begin{array}{l}{z}_{\text{Women}}=\frac{70-64}{2.5}\\ =2.4\\ z_{\text{Men}}=\frac{74-69.1}{2.8}\\ =1.75\end{array}$

Thus, the women z -score is harder to qualify the membership for Beanstalk than men’s height. So, men are more likely to qualify for Beanstalk membership.