Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q. 43 (page 379)

Based on the analysis in Exercise 41, the ferry company decides to increase the cost of a trip to $6. We can calculate the company’s profit Yon a randomly selected trip from the number of cars X. Find the mean and standard deviation ofY. Show your work.

Short Answer

Expert verified

The mean and standard deviation are

μY=3.22

σY=7.74

Step by step solution

01

Given Information

Given in the question that

μX=3.87

σX=1.29

02

Explanation

The earnings per car Xis $6and the costs is $20:

Y=6X-20

Properties mean and standard deviation:

μaX+b=aμX+b

σaX+b=aσX

Then we obtain for Y=6X-20:

localid="1649908128618" μY=μ6X-20=6μX-20=6(3.87)-20=3.22

localid="1649908143820" σY=σ6X-20=6σX=6(1.29)=7.74

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

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.

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.

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.

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.

Flip a coin. If it's headed, roll a 6-sided die. If it's tails, roll an 8-sided die. Repeat this process 5times. Let W=the number of 5's you roll.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics 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