Question

Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally​ distributed, with a mean of 111 pounds and a standard deviation of 38.7 pounds. Random samples of size 17 are drawn from this population and the mean of each sample is determined. mu Subscript x overbarequals nothing sigma Subscript x overbarequals nothing ​(Round to three decimal places as​ needed.) Sketch a graph of the sampling distribution. Choose the correct graph below. A. 111 92.2 129.8 x overbar A normal curve is over a horizontal x overbar axis labeled from 92.2 to 129.8 and is centered on 111. B. 111 82.8 139.2 x overbar A normal curve is over a horizontal x overbar axis labeled from 82.8 to 139.2 and is centered on 111. C. 9.4 -323.6 342.4 x overbar A normal curve is over a horizontal x overbar axis labeled from negative 323.6 to 342.4 and is centered on 9.4. D. 9.4 -101.6 120.4 x overbar A normal curve is over a horizontal x overbar axis labeled from negative 101.6 to 120.4 and is centered on 9.4. Click to select your answer(s).

Answer 1

The mean of the sampling distribution is equal to the population mean hence it is equal to 111 and the standard error of the mean of the sampling distribution is population standard deviation divided by the square root of sample size hence it is 38.7/sqrt(17) = 9.4

The three-sigma limits for the sampling distribution will be:

111 +/- 3*9.4 = (82.8, 139.2)

Therefore, the correct option is

B. 111 82.8 139.2 x overbar A normal curve is over a horizontal x overbar axis labeled from 82.8 to 139.2 and is centered on 111.

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