Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q24E (page 314)

Salary of a travel management professional. According to the most recent Global Business Travel Association (GBTA) survey, the average base salary of a U.S. travel management professional is \(94,000. Assume that the standard deviation of such salaries is \)30,000. Consider a random sample of 50 travel management professionals and let χ¯ represent the mean salary for the sample.

  1. What isμχ¯?
  2. What isσχ¯?
  3. Describe the shape of the sampling distribution ofχ¯.
  4. Find the z-score for the valueχ¯=86,660
  5. FindPχ¯>86,660.

Short Answer

Expert verified

Anyone who makes a career doing anything that needs a specific degree of knowledge, ability, as well as experience is referred to as a professional.

Step by step solution

01

(a) The data is given below

The calculation is given below:

Given,

μ=94,000σ=30,000n=50

μχ¯=μ0=94000μχ¯=94000

02

(b) The data is given below

The calculation is given below:

σχ¯=σn=30,00050=4242.64068712≃4242.6407

σχ¯=4242.6407

03

(c) The data is given below

The calculation is given below:

As here n≥30

As a result, the sample size is sufficient to follow the normal distributions. As a result, the distribution's form is normal.

The chart is given below:

04

(d) The data is given below

The calculation is given below:

Zscore=χ-μσ/n


χ=86660μ=94000n=50

Zscore=86660-940004242.6407=-1.73

05

(e) The data is given below

The calculation is given below:

Pχ¯>8660=1-Pχ¯<8660=1-Pχ¯-μχ¯σχ¯<8660-940004242.6407=1-PZ<-1.73

Standard normal table:

=1-0.9581848=0.0418152≃0.0418Pχ¯>86660=0.0418

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

Suppose xequals the number of heads observed when asingle coin is tossed; that is, x= 0 or x= 1. The population corresponding to xis the set of 0s and 1s generated when thecoin is tossed repeatedly a large number of times. Supposewe select n= 2 observations from this population. (That is,we toss the coin twice and observe two values of x.)

  1. List the three different samples (combinations of 0s and1s) that could be obtained.
  2. Calculate the value of X¯ffor each of the samples.
  3. Show that the sample proportion of 1s, p^, is equal to X¯.
  4. List the values thatp^can assume, and find the probabilitiesof observing these values.
  5. Construct a graph of the sampling distribution ofp^.

Tomato as a taste modifier. Miraculin is a protein naturally produced in a rare tropical fruit that can convert a sour taste into a sweet taste. Refer to the Plant Science (May 2010) investigation of the ability of a hybrid tomato plant to produce miraculin, Exercise 4.99 (p. 263). Recall that the amount x of miraculin produced in the plant had a mean of 105.3 micrograms per gram of fresh weight with a standard deviation of 8.0. Consider a random sample of n=64hybrid tomato plants and letx represent the sample mean amount of miraculin produced. Would you expect to observe a value of X less than 103 micrograms per gram of fresh weight? Explain.

Rental car fleet evaluation. National Car Rental Systems, Inc., commissioned the U.S. Automobile Club (USAC) to conduct a survey of the general condition of the cars rented to the public by Hertz, Avis, National, and Budget Rent-a-Car.* USAC officials evaluate each company’s cars using a demerit point system. Each car starts with a perfect score of 0 points and incurs demerit points for each discrepancy noted by the inspectors. One measure of the overall condition of a company’s cars is the mean of all scores received by the company (i.e., the company’s fleet mean score). To estimate the fleet mean score of each rental car company, 10 major airports were randomly selected, and 10 cars from each company were randomly rented for inspection from each airport by USAC officials (i.e., a sample of size n = 100 cars from each company’s fleet was drawn and inspected).

a. Describe the sampling distribution of x, the mean score of a sample of n = 100 rental cars.

b. Interpret the mean of x in the context of this problem.

c. Assumeμ=30 and σ=60for one rental car company. For this company, findPx¯⩾45 .

d. Refer to part c. The company claims that their true fleet mean score “couldn’t possibly be as high as 30.” The sample mean score tabulated by USAC for this company was 45. Does this result tend to support or refute the claim? Explain.

Question:Quality control. Refer to Exercise 5.68. The mean diameter of the bearings produced by the machine is supposed to be .5 inch. The company decides to use the sample mean from Exercise 5.68 to decide whether the process is in control (i.e., whether it is producing bearings with a mean diameter of .5 inch). The machine will be considered out of control if the mean of the sample of n = 25 diameters is less than .4994 inch or larger than .5006 inch. If the true mean diameter of the bearings produced by the machine is .501 inch, what is the approximate probability that the test will imply that the process is out of control?

Suppose a random sample of n measurements is selected from a population with u=100mean and variance role="math" localid="1657967387987" σ2=100. For each of the following values of n, give the mean and standard deviation of the sampling distribution of the sample mean.

  1. role="math" localid="1657967260825" n=4
  2. n=25
  3. n=100
  4. n=50
  5. n=500
  6. n=1000
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

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