Chapter 6 Review

In one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x, recorded for each sample. Which of the following is the best description of the sampling distribution of x ?

• Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 days

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 day

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 day

• Approximately normal with mean 5.5 days and standard deviation 2.6 days

• Approximately normal with mean 5.5 days and standard deviation 0.26 day

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Let X be a random variable that has a skewed distribution with mean µ = 10 and standard deviation σ = 10. Based on random samples of size 400, the sampling distribution of X is

• highly skewed with mean 10 and standard deviation 10

• highly skewed with mean 10 and standard deviation 5

• highly skewed with mean 10 and standard deviation 0.5

• approximately normal with mean 10 and standard deviation 10

• approximately normal with mean 10 and standard deviation 0.5

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There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

• Approximately normal with mean $206,274 and standard deviation $3,788

• Approximately normal with mean $206,274 and standard deviation $37,881

• Approximately normal with mean $206,274 and standard deviation $520

• Strongly right-skewed with mean $206,274 and standard deviation $3,788

• Strongly right-skewed with mean $206,274 and standard deviation $37,881

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A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

• 0.1151

• 0.2738

• 0.7257

• 0.8849

• Based on the values of the true mean and true standard deviation, it can be concluded that the population distribution is not normal and therefore the probability cannot be calculated.

A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 of the manufacturer’s batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem?

• The distribution of the number of recharge cycles for the sample is approximately normal because the population mean of 400 is greater than 30.

• The distribution of the number of recharge cycles for the sample is approximately normal because the sample size of 100 is greater than 30.

• The distribution of the number of recharge cycles for the population is approximately normal because the sample size of 100 is greater than 30.

• The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.

• The distribution of the sample means of the number of recharge cycles is approximately normal because the population mean of 400 is greater than 30.

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The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week. Let p-hat be the proportion of people in the sample who attended church. A newspaper report claims that 40% of all U.S. adults went to church last week. Suppose this claim is true.

What is the mean of the sampling distribution of p-hat?

• 0.4

• 0.44

• 0.56

• 0.6

28% of all Woodrow students believe Monday will be snow day. You take a sample of 50 students and find that 15 of them believe Monday will be a snow day. What does 50 represent? 

• n
• P
• phat
• standard deviation

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These symbols represent the mean and standard deviation for which of the following distributions?

• The Population
• The Sample
• The Sampling Distribution

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CCSS.HSS.ID.A.3

CCSS.HSS.ID.A.4

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population
• The Sample
• The Sampling Distribution

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CCSS.HSS.ID.A.2

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These symbols represent the mean and standard deviation for which of the following distributions?

• The Population
• The Sample
• The Sampling Distribution

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CCSS.HSS.ID.A.4