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Chapter 5: Q18E (page 314)

A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and a standard deviation equal to 16

a. Give the mean and standard deviation of the (repeated) sampling distribution of x.

b. Describe the shape of the sampling distribution of x. Does your answer depend on the sample size?

c. Calculate the standard normal z-score corresponding to a value of x = 15.5.

d. Calculate the standard normal z-score corresponding to x = 23

Short Answer

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Answer

The standard deviation is commonly utilized as a measurement of an asset's comparative volatility. The standard deviation is determined as the square root of the variation by calculating the departure of every observation point from the mean.

Step by step solution

01

Step-by-Step Solution Step 1: (a) The data is given below

The calculation is given below:

μX=20σX=σn=1664=2

02

(b) The data is given below

Step 3: (c) The data is given below of x will have the form of a bell-shaped normally distributed. Yes, it is dependent on the scale of the sample. As the sample size improves the sample size approaches being normal.

03

(c) The data is given below

The calculation is given below:

z =X−μσ/n=15.5−202=−2.25

04

(d) The data is given below

The calculation is given below:

z =X−μσ/n=23−202=1.5

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Most popular questions from this chapter

Question:A random sample of n = 500 observations is selected from a binomial population with p = .35.

a. Give the mean and standard deviation of the (repeated) sampling distribution ofp^the sample proportion of successes for the 500 observations.

b. Describe the shape of the sampling distribution of p^. Does your answer depend on the sample size?

A random sample of n= 300 observations is selectedfrom a binomial population with p= .8. Approximateeach of the following probabilities:

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Question:Stock market participation and IQ. Refer to The Journal of Finance (December 2011) study of whether the decision to invest in the stock market is dependent on IQ, Exercise 3.46 (p. 182). The researchers found that the probability of a Finnish citizen investing in the stock market differed depending on IQ score. For those with a high IQ score, the probability is .44; for those with an average IQ score, the probability is .26; and for those with a low IQ score, the probability is .14.

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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.

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