Feature movie lengths (in hours) were measured for all movies shown in the past

Question

Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours. If we create a sampling distribution of sample means, what would be the mean and standard deviation of that distribution given the sample size of 20? Select one: a. The mean length would be 1.80 hours with a standard deviation of 0.18 hours. b. The mean length would be 1.80 hours with a standard deviation of 0.15 hours. c. The mean length would be 1.72 hours with a standard deviation of 0.18 hours. d. The mean length would be 1.80 hours with a standard deviation of 0.034 hours.

Explanation / Answer

Answer

d. The mean length would be 1.80 hours with a standard deviation of 0.034 hours.

Hint:

By Central Limit Theorem,

Mean of the sampling distribution = population mean = 1.80 hours

Standard deviation of the sampling distribution = 0.15/SQRT (20) = 0.034

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