Chapter 12.7, Problem 17PPS

a

To determine

To calculate: the probabilities associated with the number of students who own a laptop

Explanation of Solution

Given information:

95% of high school students own a laptop

Calculation:

The probabilities associated with the number of students who own a laptop is shown in following probabilities

$x$	$P\left(X=x\right)$
0	0
1	0
2	0
3	0.00000008
4	0.00000267
5	0.00006094
6	0.00096481
7	0.01047506
8	0.0746348
9	0.3151247
10	0.59873694

b

To determine

To calculate: the probabilities that at least 8 of the 10 students own a laptop

Answer to Problem 17PPS

The required probability is 0.9885

Explanation of Solution

Given information:

95% of high school students own a laptop

Calculation:

The probability that at least 8 of the 10 students own a laptop is,

  $\begin{array}{l}P(X\ge 8)=1-P(X\le 7)\\ $ =1-{\displaystyle \sum }_{x=0}^7\left(\begin{array}{c}10\\ x\end{array}\right){(0.95)}^x{(0.05)}^{10-x}$=1-0.0115\\ =0.9885\end{array}$

Hence, the required probability is 0.9885