Chapter 8.1, Problem 8.14E

(a)

To determine

To explain what the sampling distribution tells us about the result of our sample.

Explanation of Solution

It tells us which percentages of all college students applied to colleges besides the one they are attending are most likely.

(b)

To determine

To calculate what percent of many samples would have a $\widehat{p}$ larger than $0.77$ and explain why this percent is the probability of an outcome larger than $0.77$ .

Answer to Problem 8.14E

  $2.5\%$

Explanation of Solution

$0.77$ is two standard deviations from the mean thus we know that $47.5\%$ lies between $0.77$ and the mean. We also know that $50\%$ lies before the mean and the total probability is $100\%$ . Thus the probability is then:

  $100\%-50\%-47.5\%=2.5\%$

(c)

To determine

To calculate the probability that your sample result will be either less than $0.73\text{ or greater than 0}\text{.75}$ .

Answer to Problem 8.14E

  $22.5\%$

Explanation of Solution

Since $0.73$ is two standard deviations from the mean we know that $47.5\%$ lies between $0.73\text{ and 0}\text{.75}$ and the total probability is $100\%$ . Thus the probability is then:

  $100\%-47.5\%=22.5\%$

To determine

(d)

To explain would you be surprised if the sample proportion who said they applied to another college was $\widehat{p}=0.725$ .

Explanation of Solution

No, because $0.725$ lies within three standard deviation from the mean and $99.7\%$ of the results will lie within three standard deviation from the mean.