Chapter PIV, Problem 25RE

(a)

To determine

To explain: that there is clearly a mistake in the analysis on the basis of given information.

Explanation of Solution

According to a new Gallup study, 93% of teenagers use the internet. But there are variations in how teenage boys and girls claim computers are used. The telephone survey showed that 77 percent of boys had played video games in the past week, compared to 65 percent of girls. On the other hand, compared to just 65 percent of boys, 76 of girls said they had e-mailed friends in the past week.

Many do both, so more than 100 percent of the categories can be done.

(b)

To determine

To explain: it is mutually exclusive to play the games and use e-mail.

Explanation of Solution

According to a new Gallup study, 93% of teenagers use the internet. But there are variations in how teenage boys and girls claim computers are used. The telephone survey showed that 77 percent of boys had played video games in the past week, compared to 65 percent of girls. On the other hand, compared to just 65 percent of boys, 76 of girls said they had e-mailed friends in the past week.

No, if they were, they wouldn't be disjointed, the sum would be 100% or less.

(c)

To determine

To explain: that it is independent of being a boy or a girl if a child e-mails friend.

Explanation of Solution

According to a new Gallup study, 93% of teenagers use the internet. But there are variations in how teenage boys and girls claim computers are used. The telephone survey showed that 77 percent of boys had played video games in the past week, compared to 65 percent of girls. On the other hand, compared to just 65 percent of boys, 76 of girls said they had e-mailed friends in the past week.

No, the chances for boys and girls are different.

(d)

To determine

To Calculate: The probability of 5 interviews being needed before the first person who does not use the internet is identified.

Explanation of Solution

According to a new Gallup study, 93% of teenagers use the internet. But there are variations in how teenage boys and girls claim computers are used. The telephone survey showed that 77 percent of boys had played video games in the past week, compared to 65 percent of girls. On the other hand, compared to just 65 percent of boys, 76 of girls said they had e-mailed friends in the past week.

Calculation:

Probability of the first person in 5 interviews who does not use the internet.

  $\begin{array}{c}p=0.07\\ q=0.93\\ P\left(X=5\right)=\left(0.07\right){\left(0.93\right)}^4\\ =0.0524\end{array}$