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Chapter 6: Q 30. (page 373)

Ace! Professional tennis player Novak Djokovic hits the ball extremely hard. His first-

serve speeds follow an approximately Normal distribution with mean 115milesper hour

(mph) and standard deviation 6mph. Choose one of Djokovic鈥檚 first serves at random. Let

Y = its speed, measured in miles per hour.

a. Write the event 鈥渟peed is between 100 and 120 miles per hour鈥� in terms of Y. Then find

this probability.

b. Find the value of c such that P(Y鈮�c)=0.15

Short Answer

Expert verified

a) The probability for the event 鈥渟peed is between 100 and 120 miles per hour鈥� in terms of Y is 79.05%.

b) The units of the data values are miles per hour and thusc=108.76.

Step by step solution

01

Step 1. Given information. 

We have given values of mean渭=115 standard deviation 蟽=6and x=100or120

Let Yrepresents the speed.

02

 a) Step 2. To find the probability. 

The z- score is the value decreased by the mean, divided by the standard deviation .

z=x-渭蟽=100-1156=-2.50z=x-渭蟽=120-1156鈮�0.83

Now,

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%

03

b) Step 3.To find the value of c. 

We have,

P(Y鈮�c)=0.15z=-1.0+.04z=-1.04

Now,

z=x-渭蟽=c-1156c-1156=-1.04c-115=-1.04(6)c=115-1.04(6)c=108.76

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