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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炉. 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

Cereal A company's cereal boxes advertise that each box contains 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean 渭=9.70 ounces and standard deviation 蟽=0.03 ounce.

a. What is the probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal?

b. Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal in these boxes is less than 9.65 ounces?

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.

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.

Bag check Thousands of travelers pass through the airport in Guadalajara, Mexico, each day. Before leaving the airport, each passenger must pass through the customs inspection area. Customs agents want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every traveler's luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light flashes, the passenger will be searched by customs agents. A green light means "Go ahead." Customs agents claim that 30%of all travelers will be stopped (red light), because the light has probability of showing red on any push of the button. To test this claim, a concerned citizen watches a random sample of 100 travelers push the button. Only 20 get a red light.

a. Assume that the customs agents' claim is true. Find the probability that the proportion of travelers who get a red light in a random sample of 100 travelers is less than or equal to the result in this sample.

b. Based on your results in part (a), is there convincing evidence that less than 30%of all travelers will be stopped? Explain your reasoning.

Cold cabin? The dotplot shows the results of taking 300SRSs of 10temperature readings from a Normal population with 渭渭=50and 蟽蟽=3and recording the sample standard deviation sxsxeach time. Suppose that the standard deviation from an actual sample is sx=5掳F.sx=5掳F. What would you conclude about the thermostat manufacturer's claim? Explain your reasoning.
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