1.A simple random sample is taken from a normal population. Choose the one statement that is true.

a.We can never ensure that the distribution of the sample mean isnormal or approximately normal.

b.If the sample mean equals the population mean, then the distribution of the sample mean must benormal or approximately normal.

c.We can be certain that the sample mean is normal or approximately normal only if the sample size is greater than 30.

d.For any sample size, the distribution of the sample mean is normal or approximately normal.

2.A simple random sample is taken from a left-skewed population. Choose the one statement that is true.

a.We can never ensure that the distribution of the sample mean isnormal or approximately normal.

b.If the sample mean equals the population mean, then the distribution of the sample mean must benormal or approximately normal.

c.We can be certain that the sample mean is normal or approximately normal only if the sample size is greater than 30.

d.For any sample size, the distribution of the sample mean is normal or approximately normal.

3.The distribution of incomes in a certain town is known to be right skewed with a mean of 50 thousand dollars and a standard deviation of 8 thousand dollars. If a random sample of size 40 is taken:

a.What is the shape of the distribution ofthe sample mean,?

b.What is the mean and standard deviation of the distribution of the sample mean,?

c.What is the probability that sample meanwill be between 47thousand dollarsand 48thousand dollars?

d.What is the probability that sample meanwill be greater than 56 thousand dollars?