The mean height, for a probability distribution of heights is 65 inches and the

Question

The mean height, for a probability distribution of heights is 65 inches and the standard deviation is 3 inches.

a) If a random sample of 16 people is obtained from the above population, can the sampling distribution of sample means be assumed to have a normal distribution? Why or why not?

b) If a random sample of 40 people is obtained from the above population, can the sampling distribution  of sample means be assumed to have a normal distribution? Why or why not?

c) If a normal probability distribution of heights is given, can the sampling distribution of sample means for a sample size of 16 be assumed to have a normal distribution? Why or why not?

Explanation / Answer

a) If a random sample of 16 people is obtained from the above population, can the sampling distribution of sample means be assumed to have a normal distribution? Why or why not?

No. Because the minimum sample size for normal distribution would be 30. The sample has only 16 values.

b) If a random sample of 40 people is obtained from the above population, can the sampling distribution  of sample means be assumed to have a normal distribution? Why or why not?

Yes because the sample has more than 30 values.

c) If a normal probability distribution of heights is given, can the sampling distribution of sample means for a sample size of 16 be assumed to have a normal distribution? Why or why not?

Yes, once the values are normalized, the sample size of 16 is no longer a concern.

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