Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q.6.57 (page 388)

The life of Sunshine CD players is normally distributed with a mean of 4.1years and a standard deviation of 1.3years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts. Find the probability that a CD player will break down during the guarantee period.

a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.

b. P(0<x<____________)=___________(Use zero for the minimum value of x.)

Short Answer

Expert verified
  1. The graph for the P(0<x<3)is

b. The value of theP(0<x<3)is0.1979.

Step by step solution

01

Given information (Part a)

Given in the question that

Mean=4.1

Standard deviation=1.3

02

Solution (Part a)

The graph for the P(0<x<3)with the shaded region is given below

03

Given information (Part b)

Given in the question that

Mean=4.1

Standard deviation=1.3

04

Solution (Part b)

Here we need to calculate the probability is below,

P(0<x<3)=P(x<3)−P(x<0)

=Px−μσ<3−μσ−Px−μσ<0−μσ

=PZ<3−4.11.3−PZ<0−4.11.3

=P(Z<−0.8462)−P(Z<−3.1538)

=0.1987−0.0008From standardnormal table

=0.1979

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

According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66inches and a standard deviation of 2.5inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual.

a.X~_____(_____,_____)

b. Find the probability that the person is between 65and 69inches. Include a sketch of the graph, and write a probability statement.

c. Would you expect to meet many Asian adult males over 72 inches? Explain why or why not, and justify your answer numerically.

What is the z-score of x, when x=1and X~N(12,3)?

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.

What is the z-score for a patient who takes ten days to recover?

a. 1.5

b. 0.2

c. 2.2

d. 7.3

What is the z-score of x= 9, if it is 1.5 standard deviations to the left of the mean?

In the 1992 presidential election, Alaska's 40 election districts averaged 1,956.8 votes per district for President Clinton. The standard deviation was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X=the number of votes for President Clinton for an election district be known.

a. State the approximate distribution of X

b. Is 1,956.8a population mean or a sample mean? How do you know?

c. Find the probability that a randomly selected district had fewer than 1,600votes for President Clinton. Sketch the graph and write the probability statement.

d. Find the probability that a randomly selected district had between 1,800and 2,000votes for President Clinton.

e. Find the third quartile for votes for President Clinton.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

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