The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. If the scores at this school have the same distribution as national scores.

(a) What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?(b) What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students?(c) What is the sampling distribution of the sample mean score for a random sample of 36 students?

a. mean=18.6

b. standard deviation=1.0

c. The distribution is a symmetry and mound-shaped but nowhere near normal.

Step-by-step explanation:

a. let be the sample mean.

-For a normal distributed sample, the population mean is equal to the sample mean:

Hence, the sample mean is 18.6

b. Let s denote the sample standard deviation.

-For a normally distributed population, the sample standard deviation is calculated using the formula;

Hence, the sample standard deviation is 1.0

c. The sample has a mean of 18.6 and a standard deviation of 1.0

-Since it's derived from a normally distribted population, it will be symmetrical and have an almost normal shape.

-Hence, it is a symmetry and mound-shaped, but Not Normal.

1696 hundred thousand

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