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Chapter 7: Q. 76 (page 481)

The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that

a. as we look at more and more bulbs, their average burnout time gets ever closer to the mean μ for all bulbs of this type.

b. the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution.

c. the average burnout time of a large number of bulbs has a sampling distribution with a similar shape but not as extreme (skewed, but not as strongly) as the population distribution.

d. the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

e. the average burnout time of a large number of bulbs has a sampling distribution that is exactly Normal.

Short Answer

Expert verified

(d). the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

Step by step solution

01

Given Information

The amount of time a lightbulb lasts before it burns out varies from bulb to bulb. Burnout times are heavily biassed to the right across the population.

02

Explanation for correct option

If the sample size is higher than or equal to 30, the sampling distribution of the sample mean will be nearly normal with mean and standard deviation, σ/naccording to the central limit theorem.

Therefore, the correct option is (d)

03

Explanation for incorrect option

a. as we look at more and more bulbs, their average burnout time gets ever closer to the mean for all bulbs of this type is not the correct answer

b. the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution is not the correct answer

c. the average burnout time of a large number of bulbs has a sampling distribution with a similar shape but not as extreme (skewed, but not as strongly) as the population distribution is not the correct answer.

d. the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal is not the correct answer

e. the average burnout time of a large number of bulbs has a sampling distribution that is exactly Normal is not the correct answer

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Most popular questions from this chapter

According to the U.S. Census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100 adults in a certain section of the county found that 65 owned their home. Which one of the following represents the approximate probability of obtaining a sample of 100 adults in which 65 or fewer own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?

a. (10065)(0.71)65(0.29)3510065(0.71)65(0.29)35

b. (10065)(0.29)65(0.71)3510065(0.29)65(0.71)35

c.

P(z≤0.65-0.71(0.71)(0.29)100)Pz≤0.65-0.71(0.71)(0.29)100

d.P(z≤0.65-0.71(0.65)(0.35)100)Pz≤0.65-0.71(0.65)(0.35)100

e.P(z≤0.65-0.71(0.71)(0.29)100)Pz≤0.65-0.71(0.71)(0.29)100

The mean of this distribution (don’t try to find it) will be

a. very close to the median.

b. greater than the median.

c. less than the median.

d. You can’t say, because the distribution isn’t symmetric.

e. You can’t say, because the distribution isn’t Normal.

Sample medians List all 10possible SRSs of size n=3, calculate the median quiz score for each sample, and display the sampling distribution of the sample median on a dotplot.

A statistic is an unbiased estimator of a parameter when

a. the statistic is calculated from a random sample.

b. in a single sample, the value of the statistic is equal to the value of the parameter.

c. in many samples, the values of the statistic are very close to the value of the

parameter.

d. in many samples, the values of the statistic are centered at the value of the parameter.

e. in many samples, the distribution of the statistic has a shape that is approximately

Normal.

A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value (\(500,\)100,\(25) or the statement "This ticket is not a winner." Monetary prizes can be redeemed for groceries at the store. Here is the probability distribution of the amount won on a randomly selected ticket:

Which of the following are the mean and standard deviation, respectively, of the winnings?

a. \)15.00,\(2900.00

b. \)15.00,\(53.85

c. \)15.00,\(26.93

d. \)156.25,\(53.85

e. \)156.25,$26.93
See all solutions

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