Chapter 7.2, Problem 40E

(a)

To determine

To Explain: 10% condition met in this case.

Answer to Problem 40E

Yes

Explanation of Solution

Yes, because the sample size of 7 is less than $10\%$ of the population size of 100

(b)

To determine

To Explain: the large counts condition met in this case.

Answer to Problem 40E

No

Explanation of Solution

Given:

  $\begin{array}{c}p\text{=Population proportion = }\frac{\text{Number of vowels}}{\text{Number of tiles}}=\frac{42}{100}=0.42\\ n=\text{Sample size =7}\text{.}\end{array}$

Calculation:

The sampling distribution of the sample proportion $\widehat{p}$ is approximately Normal is the large counts condition is satisfied, that is, when $np\ge 10$ and $n(1-p)\ge 10$ .

  $\begin{array}{c}np=7\left(0.42\right)=2.94<10\\ n\left(1-p\right)=7\left(1-0.42\right)=4.06<10\end{array}$

It is observed that the large counts condition is not satisfied.