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Solution to Exercise 3.48.

Let X be the number coming to a complete stop of of 20 randomly chosen drivers. Then according to the information given, $X \sim Bin(20,.2)$ .

(a) Directly from the table on p. 719:

$\begin{displaymath} P[ X \le 6 ] \; = \; .913.\end{displaymath}$

(b)

$\begin{displaymath} P[ X = 6 ] \; = \; P[ X \le 6 ] - P[ X \le 5 ] \; = \; .913 - .804 \; = \; .109 .\end{displaymath}$

(c)

$\begin{displaymath} P[ X \ge 6 ] \; = \; 1 - P[ X \le 5 ] \; = \; 1 - .804 \; = \; .196 .\end{displaymath}$

(d)

$\begin{displaymath} E[X] \; = \; 20 * .2 \; = \; 6 .\end{displaymath}$

Dennis Cox
2/19/2001