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Chapter 5: Q4E (page 303)

Refer to Exercise 5.3 and find E=(x)=μ. Then use the sampling distribution ofxfound in Exercise 5.3 to find the expected value ofx. Note thatE=(x)=μ.

Short Answer

Expert verified

E=(x)=2.7

Step by step solution

01

Determination of the probabilities of the means

The list of the probabilities found in Exercise 5.3 is shown below.

Mean

Probability

1

0.04

1.5

0.12

2

0.17

2.5

0.20

3

0.20

3.5

0.14

4

0.08

4.5

0.04

5

0.01

02

Calculation of Ex

The calculation of E(x)is shown below.

E(x)=∑[xpx]=1×0.04+1.5×0.12+2×0.17+2.5×0.20+3×0.20+3.5×0.14+4×0.08+4.5×0.04+5×0.01=0.04+0.18+0.34+0.50+0.60+0.49+0.32+0.18+0.05=2.7

Here, x= variables, and p(x)=probabilities.

Therefore, the final answer is 2.7.

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Most popular questions from this chapter

Will the sampling distribution ofχ¯ always be approximately normally distributed? Explain

A random sample ofn=100observations is selected from a population withμ=30and σ=16. Approximate the following probabilities:

a.P=(x≥28)

b.localid="1658061042663" P=(22.1≤x≤26.8)

c.localid="1658061423518" P=(x≤28.2)

d.P=(x≥27.0)

Refer to Exercise 5.3.

  1. Show thatx⇀is an unbiased estimator of.
  2. Findσx2.
  3. Find the probability that x will fall within2σxofμ.

Question: Consider the following probability distribution:


a. Findμand σ2.

b. Find the sampling distribution of the sample mean x for a random sample of n = 2 measurements from this distribution

c. Show thatxis an unbiased estimator of μ. [Hint: Show that∑(x)=∑xp(x)=μ. ]

d. Find the sampling distribution of the sample variances2for a random sample of n = 2 measurements from this distribution.

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.
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