Chapter 8.1, Problem 8.13E

(a)

To determine

To explain what percent of many samples will have a sample proportion who jog that is $0.5$ or less and explain why this is $0.5$ or less.

Answer to Problem 8.13E

  $50\%$

Explanation of Solution

$50\%$ of many samples will have a sample proportion who jog that is $0.5$ or less because the normal distribution is symmetric about its mean.

(b)

To determine

To calculate the probability that $\widehat{p}$ will take a value between $0.141\text{ and 0}\text{.159}$ .

Answer to Problem 8.13E

  $68\%$

Explanation of Solution

$68\%$ will take a value between $0.141\text{ and 0}\text{.159}$ because $68\%$ of the data of a normal distribution lies within one standard from the mean.

(c)

To determine

To calculate the probability that $\widehat{p}$ does not liebetween $0.141\text{ and 0}\text{.159}$ .

Answer to Problem 8.13E

  $32\%$

Explanation of Solution

$32\%$ of the probability does not lie between $0.141\text{ and 0}\text{.159}$ because the total probability is $100\%$ and

  $100\%-68\%=32\%$

To determine

(d)

To explain would you be surprised if the sample proportion who said they jogged was $\widehat{p}=0.17$ .

Explanation of Solution

No, because it lies within three standard deviations of the mean which is were $99.7\%$ of the results will lie.