Chapter 7.2, Problem 1.3CYU

To determine

To find: Whether the sampling distribution of $\widehat{p}$ is approximately normal or not.

Answer to Problem 1.3CYU

Yes, it is approximately normal.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Population proportion}\left(p\right)=75\%=0.75\\ \text{Sample size}\left(n\right)=1000\end{array}$

Concept used:

The sampling distribution is said to be approximately normal, if following condition is satisfied:

  $\begin{array}{l}np\ge 10\\ n\left(1-p\right)\ge 10\end{array}$

Calculation:

Here,

  $\begin{array}{c}np=1000\left(0.75\right)\\ =750\\ >10\end{array}$

And,

  $\begin{array}{c}n\left(1-p\right)=1000\left(1-0.75\right)\\ =250\\ >10\end{array}$

Thus, the sampling distribution of $\widehat{p}$ is approximately normal