Question: Random samples of size 64 are taken from a large population whose mean is 160 and whose standard deviation is 25. What is the mean of the sampling distribution of the sample mean?

(a) Referring to problem 1_3.3, what is the standard error of the sampling distribution of the sample mean?

(b) Referring to problem 1_3.3, what is the probability that the sample mean is at least 158?

(c) Referring to problem 1_3.3, what is the probability that the sample mean lies between 155 and 165?

(d) Referring to problem 1_3.3, if the sample mean was actually 150, would you consider that unusual?