Log out Go to App
Go to App

Learning Materials

Features

Discover

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’s first serves at random. Let

Y = its speed, measured in miles per hour.

a. Write the event “speed is between 100 and 120 miles per hour” in terms of Y. Then find

this probability.

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

Short Answer

Expert verified

a) The probability for the event “speed is between 100 and 120 miles per hour” 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 meanμ=115 standard deviation σ=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-μσ=100-1156=-2.50z=x-μσ=120-1156≈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≤c)=0.15z=-1.0+.04z=-1.04

Now,

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

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Using Benford's law According to Benford's law (Exercise 15, page 377), the probability that the first digit of the amount of a randomly chosen invoice is an 8 or a 9 is 0.097. Suppose you examine randomly selected invoices from a vendor until you find one whose amount begins with an 8 or a 9 .

a. How many invoices do you expect to examine before finding one that begins with an 8 or 9 ?

b. In fact, the first invoice you find with an amount that starts with an 8 or 9 is the 40 th invoice. Does this result provide convincing evidence that the invoice amounts are not genuine? Calculate an appropriate probability to support your answer.

Get on the boat! A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y= money collected on a randomly selected ferry trip is shown here. From Exercise 7, μY=$19.35.

(a) Find the median of Y.

(b) Compare the mean and median. Explain why this relationship makes sense based on the probability distribution.

Baby elk Refer to Exercise 77 . How surprising would it be for more than 4 elk in the sample to survive to adulthood? Calculate an appropriate probability to support your answer.

.Life insurance The risk of insuring one person’s life is reduced if we insure many people. Suppose that we insure two 21-year-old males, and that their ages at death are independent. If X1andX2are the insurer’s income from the two insurance policies, the insurer’s average income W on the two policies is

W=X1+X22=0.5X1+0.5X2

Find the mean and standard deviation of W. (You see that the mean income is the same as for a single policy but the standard deviation is less.)

Take a spin Refer to Exercise 83. Calculate and interpret P(X≤7)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free