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Solution to Exercise 3.46.

We use the table on p. 720.

(a)

$\begin{displaymath} P[X \le 2] \; = \; 0.873 .\end{displaymath}$

(b)

$\begin{displaymath} P[X \ge 5] \; = \; 1 - P[X < 5] \; = \; 1 - P[X \le 4] \; = \; 1 - .993 \; = \; 0.007 .\end{displaymath}$

(c)

$\begin{displaymath} P[1 \le X \le 4] \; = \; P[X \le 4] - P[ X < 1] \; = \; .993 - .277 \; = \; .716 .\end{displaymath}$

(d)

$\begin{displaymath} P[X = 0] \; = \; .277 .\end{displaymath}$

(e)

$\begin{displaymath} E[X] \; = \; 25 * .05 \; = \; 1.25 .\end{displaymath}$

$\begin{displaymath} \sigma_X \; = \; \sqrt{25*.05*(1-.05)} \; = \; 1.0897 .\end{displaymath}$

Dennis Cox
2/11/2001