Chapter 6.3, Problem 104E

a.

To determine

To explain: The reason of D being normally distributed.

Explanation of Solution

Given:

Number of adults (n) = 100

Proportion of adults that have more debt than saving (p) = 0.24

Calculation:

Here,

  $\begin{array}{l}np=100\left(0.24\right)=24>10\\ n\left(1-p\right)=100\left(1-0.24\right)=76>10\end{array}$

Hence, the D is approximately normally distributed.

b.

To determine

To find: The probability that 30 or more adults have more debt than saving.

Explanation of Solution

The probability that 30 or more adults have more debt than savingis calculated as:

  $\begin{array}{c}P\left(X\ge 30\right)=P\left(Z\ge \frac{30-100\left(0.24\right)}{\sqrt{100\left(0.24\right)\left(1-0.24\right)}}\right)\\ =P\left(Z\ge 1.405\right)\\ =1-0.920\\ =0.08\end{array}$

Thus, the required probability is 0.08.