Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q. 4 (page 409)

T6.4. A certain vending machine offers 20-ounce bottles of soda for \(1.50.The number of bottlesXbought from the machine on any day is a random variable with mean 50and standard deviation 15.Let the random variable Yequal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?
(a) μY=\)1.50,σY=\(22.50
(b) μY=\)1.50,σY=\(33.75
(c)μY=\)75,σY=\(18.37
(d)μY=\)75,σY=\(22.50
(e) μY=\)75,σY=$33.75

Short Answer

Expert verified

The mean and standard deviation is μY=$75,σY=$22.50. So, the option(d) is correct.

Step by step solution

01

Given information

The number of bottles X is a random variable with mean 50and standard deviation 15. Let the random variable Yequal the total revenue from the machine.

02

Explanation

Given: μX=50, and μX=50
The total revenue is the income of $1.50per bottle multiplied by the number of bottles X:$Y=1.50X
Properties mean and standard deviation:

μaX+b=aμX+bσaX+b=|a|σX
The mean and standard deviation of the total revenue is then:μY=μ1.5X=1.5μX=1.5(50)=$75

σY=σ1.5X=1.5σX=1.5(15)=$22.50

Hence, option (d) μY=$75,σY=$22.50is correct.

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

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’s supposed to be? Compute P(X≤348) and use the result to justify your answer.

Binomial setting? A binomial distribution will be approximately correct as a model for one of these two sports settings and not for the other. Explain why by briefly discussing both settings. (a) A National Football League kicker has made 80%of his field-goal attempts in the past. This season he attempts 20field goals. The attempts differ widely in the distance, angle, wind, and so on. (b) A National Basketball Association player has made 80%of his free-throw attempts in the past. This season he takes 150free throws. Basketball free throws are always attempted from 15feet away with no interference from other players

Exercises 47 and 48 refer to the following setting. Two independent random variables Xand Yhave the probability distributions, means, and standard deviations shown.

48. Difference Let the random variable D=X-Y.

(a) Find all possible values of D. Compute the probability that Dtakes each of these values. Summarize the probability distribution ofD in a table.
(b) Show that the mean of Dis equal toμX-μY.
(c) Confirm that the variance of Dis equal to σX2+σY2.Find all possible values of D. Compute the probability that takes each of these values. Summarize the probability distribution of in a table.

53. The Tri - State Pick 3Refer to Exercise 42. Suppose you buy a $1 ticket on each of two different days.
(a) Find the mean and standard deviation of the total payoff. Show your work.
(b) Find the mean and standard deviation of your total winnings. Interpret each of these values in context.

Blood types In the United States, 44%of adults have type O blood. Suppose we choose 7U.S. adults at random. Let X=the number who have type O blood. Use the binomial probability formula to find P(X=4). Interpret this result in context.

See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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