/*! 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. 37 The time X it takes Hattan to dr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 37 (page 384)

The time X it takes Hattan to drive to work on a randomly selected day follows a distribution that is approximately Normal with mean 15 minutes and standard deviation 6.5 minutes. Once he parks his car in his reserved space, it takes 5 more minutes for him to walk to his office. Let T= the total time it takes Hattan to reach his office on a randomly selected day, so T=X+5. Describe the shape, center, and variability of the probability distribution of T.

Short Answer

Expert verified

T is a normal distribution with a mean of 20 and a standard deviation of 6.5 minutes.

Step by step solution

01

Given information

Given:

The time taken by Hattan to drive to work is :X

Time taken is Normal with mean : 15minutes

Standard deviation : 6.5minutes

It takes for him to walk to his office : 5minutes

T=the total time it takes Hattan to reach his office

鈬�T=X+5

02

Describing the shape, center, and variability of the probability distribution of T

Shape :

Tis a normal distribution function since adding the constant to every data value has no effect on the shape of the distribution.

Center:

When the constant is added to each data value, the center of the distribution is also enlarged, making Ta normal distribution function.

渭T=渭X+5=15+5=20

Spread:

When you add the constant to every data value, the spread of the distribution does not change; it stays the same.

蟽T=蟽X=6.5

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

Red light! Refer to Exercise 84. Calculate and interpret P(Y鈮�7)

Skee BallAna is a dedicated Skee Ball player (see photo in Exercise 4) who always rolls for the 50-point slot. The probability distribution of Ana鈥檚 score Xon a randomly selected roll of the ball is shown here. From Exercise 8, 渭X=23.8.

(a) Find the median of X.

(b) Compare the mean and median. Explain why this relationship makes sense based on the probability distribution.

During the winter months, the temperatures at the Starneses鈥� Colorado cabin can stay well below freezing (32掳For0掳C)for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes 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鈥� worth of data, the temperature Tin the cabin at midnight on a randomly selected night can be modeled by a Normal distribution with mean 8.5掳Cand standard deviation 2.25掳C. Let Y=the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall thatF=(9/5)C+32).

a. Find the mean of Y.

b. Calculate and interpret the standard deviation of Y.

c. Find the probability that the midnight temperature in the cabin is less than 40掳F.

Benford鈥檚 law and fraud

(a) Using the graph from Exercise 21, calculate the standard deviation 蟽Y. This gives us an idea of how much variation we鈥檇 expect in the employee鈥檚 expense records if he assumed that first digits from 1 to 9 were equally likely.

(b) The standard deviation of the first digits of randomly selected expense amounts that follow Benford鈥檚 law is 蟽X=2.46. Would using standard deviations be a good way to detect fraud? Explain your answer.

In debt? Refer to Exercise 100.

a. Justify why D can be approximated by a normal distribution.

b. Use a normal distribution to estimate the probability that 30or more adults in the sample have more debt than savings.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.