Chapter 10, Problem AP3.27CPT

To determine

To find out about how far do you expect the sample proportion to be from the true population from the options given in the question.

Answer to Problem AP3.27CPT

Option (c) is the correct option.

Explanation of Solution

It is given in question that, in a simple random sample of $250$ people who work in Washington, the true proportion of people who uses public transportation to get to work in Washington is $0.45$ .

As we know that, the standard deviation is composed of the true probability and the sample size. And also that, the standard deviation of the sample decreases as sample size increases. Thus, we have,

  $\begin{array}{l}\sigma =\sqrt{\frac{p(1-p)}{n}}\\ =\sqrt{\frac{0.45(1-0.45)}{250}}\\ =0.0315\end{array}$

Thus, we have that it should be $0.0315$ from the true population. Therefore, option (c) is the correct option.