Chapter 7.2, Problem 49E

To determine

To Explain: that the sampling distribution $\widehat{p}$ is approximately normal because.

Answer to Problem 49E

  $np\text{=225}\text{and}n\left(1-p\right)\text{=525}\text{are}\text{both}\text{at}\text{least}\text{10}$

Explanation of Solution

Given:

  $\begin{array}{c}p=30\%=0.30\\ n=750\end{array}$

Calculation:

  $\begin{array}{c}np=750\left(0.30\right)\\ =225\\ n\left(1-p\right)=750\left(1-0.30\right)\\ =525\end{array}$

Normal distribution is satisfied because both are at least 10 and the sampling distribution of the sample proportion is approximately normal.

Hence, the correct option is (b)