Chapter 11, Problem 11.12AYK

(a)

To determine

To find out what proportions of bladders are between $500\text{ and 600}$ ml in the adult male population using table B.

Answer to Problem 11.12AYK

  $0.3830$ .

Explanation of Solution

In the question it is given that the previous exercise described the distribution of bladder volumes in men and in women. Thus, mean and standard deviation for the men and women are as follows:

  $\begin{array}{l}{\mu }_M=550\\ {\sigma }_M=100\\ {\mu }_W=400\\ {\sigma }_W=75\end{array}$

So, we have to find out the proportions of bladders are between $500\text{ and 600}$ ml in the adult male population as:

  $\begin{array}{l}P(500<x<600)\\ =P(\frac{500-550}{100}<z<\frac{600-550}{100})\\ =P(-0.5<z<0.5)\\ =P(z<0.5)-P(z<-0.5)\\ =0.6915-0.3085\\ =0.3830\end{array}$

(b)

To determine

To find out what proportions of bladders are between $500\text{ and 600}$ ml in the adult female population using table B.

Answer to Problem 11.12AYK

  $0.08797$ .

Explanation of Solution

In the question it is given that the previous exercise described the distribution of bladder volumes in men and in women. Thus, mean and standard deviation for the men and women are as follows:

  $\begin{array}{l}{\mu }_M=550\\ {\sigma }_M=100\\ {\mu }_W=400\\ {\sigma }_W=75\end{array}$

So, we have to find out the proportions of bladders are between $500\text{ and 600}$ ml in the adult female population as:

  $\begin{array}{l}P(500<x<600)\\ =P(\frac{500-400}{75}<z<\frac{600-400}{75})\\ =P(1.33<z<2.67)\\ =P(z<2.67)-P(z<1.33)\\ =0.99621-0.90824\\ =0.08797\end{array}$

(c)

To determine

To find out how large are the largest $25\%$ of the bladder volumes in the adult male population using table B.

Answer to Problem 11.12AYK

  $617.45$ .

Explanation of Solution

In the question it is given that the previous exercise described the distribution of bladder volumes in men and in women. Thus, mean and standard deviation for the men and women are as follows:

  $\begin{array}{l}{\mu }_M=550\\ {\sigma }_M=100\\ {\mu }_W=400\\ {\sigma }_W=75\end{array}$

So, we have to find how large are the largest $25\%$ of the bladder volumes in the adult male population as:

As we know the z-score for the $25\%$ probability is $0.6745$ , then we have,

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ \Rightarrow 0.6745=\frac{x-550}{100}\\ \Rightarrow x=67.45+550\\ =617.45\end{array}$

(d)

To determine

To find out how large are the largest $25\%$ of the bladder volumes in the adult female population using table B.

Answer to Problem 11.12AYK

  $450.59$ .

Explanation of Solution

In the question it is given that the previous exercise described the distribution of bladder volumes in men and in women. Thus, mean and standard deviation for the men and women are as follows:

  $\begin{array}{l}{\mu }_M=550\\ {\sigma }_M=100\\ {\mu }_W=400\\ {\sigma }_W=75\end{array}$

So, we have to find how large are the largest $25\%$ of the bladder volumes in the adult female population as:

As we know the z-score for the $25\%$ probability is $0.6745$ , then we have,

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ \Rightarrow 0.6745=\frac{x-400}{75}\\ \Rightarrow x=50.59+400\\ =450.59\end{array}$