Chapter 15, Problem 30E

(a)

To determine

To find: the percent of the respondents were under 30 and did not snore.

Answer to Problem 30E

13.7%

Explanation of Solution

Formula used:

  $P\left(T\text{'}\cap S\text{'}\right)=1-P\left(T\cup S\right)$

Calculation:

Let T = Adult is over thirty

S = Adult snored

So that,

  $\begin{array}{c}P\left(T\right)=0.815\\ P\left(S\right)=0.368\\ P\left(S\cap T\right)=0.32\\ P\left(T\text{'}\cap S\text{'}\right)=1-P\left(T\cup S\right)\\ =1-\{0.815+0.368-0.32\}\\ =1-0.863\\ =0.137\end{array}$

About 13.7% of respondents were under 30 and did not snore.

(b)

To determine

To Explain: that the snoring is independent of age.

Explanation of Solution

Formula used:

  $P\left(S|T\right)=\frac{P\left(S\cap T\right)}{P\left(T\right)}$

Calculation:

  $\begin{array}{c}P\left(S/T\right)=\frac{P\left(S\cap T\right)}{P\left(T\right)}\\ =\frac{0.32}{0.815}\\ =0.3926\end{array}$

  $P\left(S\right)\ne P\left(S|T\right)$ Therefore snoring is not independent of Age.