Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q69SE (page 324)

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?

Short Answer

Expert verified

The probability that the test will imply that the process is out of control is 0.97725.

Step by step solution

01

Given Information

The sample size is 25

The mean is 0.501.inch

The standard deviation is 0.001.inch

The standard deviation of x¯is calculated as

σX¯=σn=0.00125=0.0002

02

Explanation

The probability is computed as

px¯<0.4994=px¯-μσn<0.4994-0.5010.0002=pz<-0.00160.0002=pz<-8=0

And

px¯>0.5006=px¯-μσn>0.5006-0.5010.0002=pz>-0.00040.0002=pz>-2=0.97725

Here we used equation 1 & 2 to get required probability

px¯<0.4994+px¯>0.5006=0+0.97725=0.97725

Hence, the probability is 0.97725.

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 a random sample of n = 500 measurements is selected from a binomial population with probability of success p. For each of the following values of p, give the mean and standard deviation of the sampling distribution of the sample proportion,p^.

  1. p= .1
  2. p= .5
  3. p= .7

Use the computer to generate 500 samples, each containing n = 25 measurements, from a population that contains values of x equal to 1, 2, . . 48, 49, 50 Assume that these values of x are equally likely. Calculate the sample mean (χ¯) and median m for each sample. Construct relative frequency histograms for the 500 values of (χ¯)and the 500 values of m. Use these approximations to the sampling distributions of (χ¯)and m to answer the following questions:

a. Does it appear that and m are unbiased estimators of the population mean? [Note:μ=25.5]

b. Which sampling distribution displays greater variation?

Refer to Exercise 5.18. Find the probability that

  1. x¯is less than 16.
  2. x¯is greater than 23.
  3. x¯is greater than 25.
  4. x¯falls between 16 and 22.
  5. x¯is less than 14.

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.

Corporate sustainability of CPA firms. Refer to the Business and Society (March 2011) study on the sustainability behaviours of CPA corporations, Exercise 1.28 (p. 51). Corporate sustainability, recall, refers to business practices designed around social and environmental considerations. The level of support senior managers has for corporate sustainability was measured quantitatively on a scale ranging from 0 to 160 points. The study provided the following information on the distribution of levels of support for sustainability:μ=68 , σ=27. Now consider a random sample of 45 senior managers and let x represent the sample mean level of support.

a. Give the value of μx¯, the mean of the sampling distribution ofx¯ , and interpret the result.

b. Give the value ofσx¯ , the standard deviation of the sampling distribution of x¯, and interpret the result.

c. What does the Central Limit Theorem say about the shape of the sampling distribution ofx¯ ?

d. Find Px¯>65.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

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