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Chapter 7: Q. T7.10 (page 438)

Suppose that you are a student aide in the library and agree to be paid according to the "random pay" system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the week is 80\(. If it comes up tails, your pay for the week is 40\). You work for the library for 100 weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings x-x¯. The shape of the sampling distribution of will be

a. Normal.

b. approximately Normal.

c. right-skewed.

d. left-skewed.

e. symmetric but not Normal.

Short Answer

Expert verified

(e). The sample distribution will be symmetric but not normal in shape.

Step by step solution

01

Given Information

The following options are

a. Normal.

b. approximately Normal.

c. right-skewed.

d. left-skewed.

e. symmetric but not Normal.

02

Explanation for correct option

A basic arbitrary sample has a duration of two weeks, with an average duration of two weeks. Because it can get 40$ during the first week, it is twice as likely to get 60$, then 40$, and finally 80$.

As a result, the distribution would be symmetric about $60, but otherwise normal.

As a result, the best solution is (e)

03

Explanation for incorrect option

a. The shape of the sampling distribution of will not be Normal

b. The shape of the sampling distribution of will not be approximately Normal

c. The shape of the sampling distribution of will not be right-skewed.

d. The shape of the sampling distribution of will not be left-skewed .

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Most popular questions from this chapter

Increasing the sample size of an opinion poll will reduce the

a. bias of the estimates made from the data collected in the poll.

b. variability of the estimates made from the data collected in the poll.

c. effect of nonresponse on the poll.

d. variability of opinions in the sample.

e. variability of opinions in the population.

A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean x-x¯. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of x-x¯will be half as big as when using a sample size of 160 . What sample size should the researcher use?

a. 40

b. 80

c. 320

d. 640

e. There is not enough information to determine the sample size.

Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. A commuter plane carries 30 passengers. Find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds.

Suppose we select an SRS of size n=100n=100from a large population having proportion p of successes. Let p∧p^be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of p∧p^?

a. 0.01

b. 0.09

c. 0.85

d. 0.975

e. 0.999

Tall girls According to the National Center for Health Statistics, the distribution of height for 16-year-old females is modeled well by a Normal density curve with mean μ=64inches and standard deviation σ=2.5inches. Assume this claim is true for the three hundred 16-year-old females at a large high school.

a. Make a graph of the population distribution.

b. Imagine one possible SRS of size 20from this population. Sketch a dotplot of the distribution of sample data.
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