Chapter 6.1, Problem 30E

(a)

To determine

To Calculate: the event in terms of Y and find its probability

Answer to Problem 30E

P (100<Y<120) =0.7905

Explanation of Solution

Given:

  $\begin{array}{c}\mu =115\\ \sigma =6\\ Y=100or120\end{array}$

Formula used:

  $z=\frac{y-\mu }{\sigma }$

Calculation:

The event between 100 and 120 miles per hour can be represented in terms Y as

100<Y<120

Z score for Y=100

  $z=\frac{100-115}{6}=-2.50$

Z score for Y=120

  $z=\frac{120-115}{6}=0.83$

Corresponding probability using the normal probability table

P (100<Y<120) =P (-2.50<Z<0.83)

  =P (Z<0.83)-P (Z<-2.50)

  =0.7967-0.0062

  =0.7905

  =79.05%

  

(b)

To determine

To Calculate: the value of c

Answer to Problem 30E

  $c=108.76$

Explanation of Solution

Given:

  $\begin{array}{l}\mu =115\\ \sigma =6\\ \text{P}\left(Y\le c\right)=0.15\end{array}$

Formula used:

  $z=\frac{y-\mu }{\sigma }$

Calculation:

  

By z table get the value of z

Z=-1.04

  $\begin{array}{c}z=\frac{y-\mu }{\sigma }\\ -1.04=\frac{c-115}{6}\\ -6.24=c-115\\ c=115-6.24\\ c=108.76\end{array}$