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Chapter 7: Q. 7.27 (page 300)

Why is obtaining the mean and standard deviation of x炉 a first step in approximating the sample distribution of the sample mean by a normal distribution?

Short Answer

Expert verified

The normal distribution always depends upon two parameters the mean and the standard deviation for any given random variable. Hence, the mean and standard deviation of x炉are obtained first when approximating the sample distribution of the sample mean by a normal distribution.

Step by step solution

01

Step 1. Given Information

The objective is to find the reason why obtaining the mean and standard deviation of x炉is a first step in approximating the sampling distribution of the sample mean by a normal distribution.

02

Step 2. Explanation

A variable is normally distributed if its distribution has the shape of a normal curve and that a normal distribution is determined by the mean and standard deviation.

Hence a first step in learning how to approximate the sampling distribution of the sample mean by a normal distribution is to obtain the mean and standard deviation of the sample mean, that is, of the variable x炉.

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Most popular questions from this chapter

What is the sampling distribution of a statistic? Why is it important?

Ethanol Railroad Tariffs. An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The Agricultural Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard deviation of such tariff rates is \(1,150, determine the probability that the mean tariff rate of 500randomly selected railroad car shipments of ethanol will be within \)100of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.

America's Riches. Each year, Forbes magazine publishes a list of the richest people in the United States. As of September l6, 2013, the six richest Americans and their wealth (to the neatest billion dollars) are as shown in the following table. Consider these six people a population of interest.

(a) For sample size of 5construct a table similar to table 7.2 on page293.(There are 6 possible sample) of size 5

(b) For a random sample of size 5determine the probability that themean wealth of the two people obtained will be within 3(i.e,3billion) of the population mean. interpret your result in terms of percentages.

Does the sample size have an effect on the mean of all possible sample means? Explain your answer.

Refer to Exercise 7.3 on page 295 .

a. Use your answers from Exercise 7.3(b) to determine the mean, 渭s. of the variable x炉 for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, 渭i, of the variable x~, using only your answer from Exercise 7.3(a).
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