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Chapter 7: Q.10 (page 460)

Suppose that you are a student aide in the library and agree to be paid according to the 鈥渞andom pay鈥� 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. The shape of the sampling distribution of xwill be

(a) Normal.

(b) approximately Normal

(c) right-skewed

(d) left-skewed.

(e) symmetric but not Normal.

Short Answer

Expert verified

The Correct answer is (e)

Step by step solution

01

Given Information

Payment for the week if the coin comes up heads=$80

Payment for the week if the coin comes up tails=$40

Number of weeks of work=100

Number of weeks for SRS = 2

02

Explanation

Given the number of the week for SRS is 2.

This means the average amount could be $40for two weeks,$80for two weeks, or $60( $40for one week and $80for the other week).

It is seen that getting $60is twice likely because on the first week $40can be obtained and $80on the second week or vice versa.

Thus, the distribution will be symmetric $60and it will also be normal.

Hence, the correct answer is (e).

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Most popular questions from this chapter

The CLT applet Go to the textbook Web site (www whfreeman com/tp4e) and click on "Statistical Applets." Launch the Central limit Theorem applet. You should see a screen like the one shown here. Click and drag the slider to change the sample size, and watch how the density curve for the sampling distribution changes with it. Write a few sentences describing what in happening.

Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) in 2003told airlines to assume that passengers average 190pounds 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 35pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 30passengers.

(a) Explain why you cannot calculate the probability that a randomly selected passenger weighs more than 200pounds.

(b) Find the probability that the total weight of the passengers on a full 铿俰ght exceeds 6000pounds. Show your work. (Hint: To apply the central limit theorem, restate the problem in terms of the mean weight.)

The name for the pattern of values that a statistic takes when we sample repeatedly from the same population is

(a) the bias of the statistic.

(b) the variability of the statistic.

(c) the population distribution.

(d) the distribution of sample data.

(e) the sampling distribution of the statistic.

The histogram above left shows the intervals (in minutes) between eruptions of the Old Faithful geyser for all 222recorded eruptions during a particular month. For this population, the median is 75minutes. We used Fathom software to take 500SRSs of size 10from the population. The 500values of the sample median are displayed in the histogram above right. The mean of the 500sample median values is 73.5.

Suppose we had taken samples of size 20instead of size 10. Would the spread of the sampling distribution be larger, smaller, or about the same? Justify your answer

Cold cabin? The Fathom screen shot below shows the results of taking 500SRSs of 10temperature readings from a population distribution that鈥檚 N(50,3)and recording the sample variance 2xeach time.

(a) Describe the approximate sampling distribution.

(b) Suppose that the variance from an actual sample is s2x=25. What would you conclude about the thermostat manufacturer鈥檚 claim? Explain
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