Question

Suppose the true proportion of people who use public transportation to get to work in the Washington, D.C. area is $0.45$. In a simple random sample of $250$people who work in Washington, about how far do you expect the sample proportion to be from the true proportion?

a. $0.4975$

b. $0.2475$

c. $0.0315$

d. $0.0009$

e.$0$

Short answer

The correct option is : (c) $0.0315$.

Step-by-step solution

- Given Information

We are given the probability of people who use public transportation to get to work in the Washington D.C. area is $0.45$and we are given a sample of $250$people . We now need to calculate standard deviation .

Explanation 

We need to find standard deviation for given sample . So,

$p$is the given probability of sample and $n$is the number of people comprising the sample .

Standard deviation $=\sqrt{\frac{p(1-p)}{n}}$$\sigma =\sqrt{\frac{p(1-p)}{n}}$

$\sigma =\sqrt{\frac{0.45(0.55)}{250}}$

$\sigma =0.0315$