Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q.24 (page 356)

Running a mile A study of 12,000able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11minutes and standard deviation 0.74 minute. Choose a student at random from this group and call his time for the mile Y. Find P(Y<6) and interpret the result. Follow the four-step process.

Short Answer

Expert verified

There is a chance of about 6.68% that the student will run a time of less than 6 minutes.

Step by step solution

01

Given Information

μ=7.11

σ=0.74

02

Explanation

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

z=x-μσ=6-7.110.74≈-1.50

Determine the corresponding probability using the normal probability table in the appendix:

P(X<6)=P(Z<-1.50)=0.0668=6.68%

There is a chance of about 6.68% that the student will run a time of less than 6 minutes.

03

Final Answer

The probability ofP(X<6)=0.0668.

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

19. Housing in San Jose How do rented housing units differ from units occupied by their owners? Here are the distributions of the number of rooms for owner-occupied units and renter-occupied units in San Jose,
California:

Let X = the number of rooms in a randomly selected owner-occupied unit and Y = the number of rooms in a randomly chosen renter-occupied unit.
(a) Make histograms suitable for comparing the probability distributions of X and Y. Describe any differences that you observe.
(b) Find the mean number of rooms for both types of housing unit. Explain why this difference makes sense.
(c) Find the standard deviations of both X and Y. Explain why this difference makes sense.

Life insurance A life insurance company sells a term insurance policy to a21-year-old male that pays 100,000if the insured dies within the next 5years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of 250each year as payment for the insurance. The amount Y that the company earns on this policy is 250per year, less the 100,000that it must pay if the insured dies. Here is a partially completed table that shows information about risk of mortality and the values of Y=profit earned by the company:

(a) Copy the table onto your paper. Fill in the missing values of Y.

(b) Find the missing probability. Show your work.

(c) Calculate the mean μY. Interpret this value in context.

Refer to the previous Check Your Understanding (page 390 ) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined X=the number of Patti's correct guesses.

1. Find μX. Interpret this value in context.

2. Find localid="1649452775386" σX. Interpret this value in context.

For each of the following situations, determine whether the given random variable has a binomial distribution. Justify your answer.

Choose three students at random from your class. Let Y=the number who are over 6feet tall.

86.1in 6wins As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each cap. Some of the caps said, “Please try again,” while others said, “You’re a winner!” The company advertised the promotion with the slogan “1in6wins a prize.” Suppose the company is telling the truth and that every 20-ounce
bottle of soda it fills has a1-in-6chance of being a winner. Seven friends each buy one 20-ounce bottle of the soda at a local convenience store. Let X= the number who win a prize.
(a) Explain why X is a binomial random variable.
(b) Find the mean and standard deviation of X. Interpret each value in context.

(c) The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or is the company’s 1-in-6 claim inaccurate? Compute P(X≥3) and use the result to justify your answer.

See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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