/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 24 24. Running a mile A study of 12... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 24 (page 356)

24. 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 0.74minute. 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

The probability is 0.0668. And there is 6.68%chances that student's run would be less than 6 minutes.

Step by step solution

01

Given information

Normal with mean 7.11minutes and standard deviation 0.74 minute.

02

Explanation

Let's say Xis a random variable that has a normal distribution with a mean of 7.11and a standard deviation of 0.74.

Thez-score is calculated by dividing the value reduced by the mean by the standard deviation:

z=x-渭蟽
Where, xindicates raw score, 渭indicates population mean, and 蟽indicates population standard deviation.

P(Y<6)can be calculated as:

P(Y<6)=Py鈭�渭蟽<9鈭�渭蟽=PZ<6鈭�7.110.74=P(Z<鈭�1.50)

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

85. Aircraft engines Engineers define reliability as the probability that an item will perform its function under specific conditions for a specific period of time. A certain model of aircraft engine is designed so that each engine has probability 0.999 of performing properly for an hour of flight. Company engineers test an SRS of 350 engines of this model. Let X= the number that operate for an hour without failure.
(a) Explain whyX is a binomial random variable.

(b) Find the mean and standard deviation ofX. Interpret each value in context.
(c) Two engines failed the test. Are you convinced that this model of engine is less reliable than it鈥檚 supposed to be? Compute P(X鈮�348) and use the result to justify your answer.

45. Too cool at the cabin? During the winter months, the temperatures at the Stameses' Colorado cabin can stay well below freezing 32掳For 0掳Cfor weeks at a time. To prevent the pipes from freezing, Mrs. Stames sets the thermostat at 50掳F. She also buys a digital thermometer that records the indoor temperature each night at midnight. Unfortunately, the thermometer is programmed to measure the temperature in degrees Celsius. Based on several years' worth of data, the temperature Tin the cabin at midnight on a randomly selected night follows a Normal distribution with mean 8.5掳Cand standard deviation2.25掳C.
(a) Let Y=the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall that F=(9/5)C+32). Find the mean and standard deviation of Y.

(b) Find the probability that the midnight temperature in the cabin is below 40掳F. Show your work.

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 渭Y. Interpret this value in context.

Chess and reading (4.3) If the study found a statistically signi铿乧ant improvement in reading scores, could you conclude that playing chess causes an increase in reading skills? Justify your answer

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 渭X. Interpret this value in context.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

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.