Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q.7.27 (page 300)

Why is obtaining the mean and standard deviation ofxa first step in approximating the sample distribution of the sample mean by a normal distribution.

Short Answer

Expert verified

To acquire the exact form of the sampling distribution (normal distant) of the sample mean, we must first obtain the values of the sample mean's mean μxand standard deviationσx.

Step by step solution

01

Given Information

We have To find The reason is obtaining the mean and standard deviation of xa First step in approximating the sampling distribution of the sample mean by a normal distribution.

02

Explanation

Means μand standard deviation σare the parameters of the normal distribution. The values of these parameters μ&σare required to establish the exact form of the normal distortion.

To acquire the exact form of the sampling distribution (normal distant) of the sample mean, we must first obtain the values of the sample mean's mean μxand standard deviation σx

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 the central limit theorem, for a relatively large sample size, the variable x~is approximately normally distributed.

a. What rule of thumb is used for deciding whether the sample size is relatively large?

b. Roughly speaking, what property of the distribution of the variable under consideration determines how large the sample size must be for a normal distribution to provide an adequate approximation to the distribution of x~ ?

In Example 7.5, we used the definition of the standard deviation of a variable to obtain the standard deviation of the heights of the five starting players on a men's basketball team and also the standard deviation of x for samples of sizes 1,2,3,4,5.The results are summarized in Table 7.6on page 298. Because the sampling is without replacement from a finite population, Equation (7.1) can also be used to obtain σx.

Part (a): Apply Equation (7.1) to compute σx for sample sizes of 1,2,3,4,5. Compare your answers with those in Table 7.6.

Part (b): Use the simpler formula, Equation (7.2) to compute σx for samples of sizes 1,2,3,4,5.Compare your answers with those in Table 7.6. Why does Equation (7.2)generally yield such poor approximations to the true values?

Part (c): What percentages of the population size are samples of sizes 1,2,3,4,5.

Testing for Content Accuracy. A brand of water-softener salt comes in packages marked "net weight 40lb." The company that packages the salt claims that the bags contain an average of 40lbof salt and that the standard deviation of the weights is 1.5lbAssume that the weights are normally distributed.

a. Obtain the probability that the weight of one randomly selected bag of water-softener salt will be 39lb or less, if the company's claim is true.

b. Determine the probability that the mean weight of 10 randomly selected bags of water-softener salt will be 39lb or less, if the company's claim is true.

c. If you bought one bag of water-softener salt and it weighed 39lb, would you consider this evidence that the company's claim is incorrect? Explain your answer.

d. If you bought 10 bags of water-softener salt and their mean weight was 39lb, would you consider this evidence that the company's claim is incorrect? Explain your answer.

Repeat parts (b)-(e) of Exercise 7.11 for samples of size5.

A variable of a population has a mean of μ=35and a standard deviation of σ=42.

a. If the variable is normally distributed, identify the sampling distribution of the sample mean for samples of size 9.

b. Can you answer part (a) if the distribution of the variable under consideration is unknown? Explain your answer.

c. Can you answer part (a) if the distribution of the variable under consideration is unknown but the sample size is 36instead of 9?

Why or why not?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

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