9. Given: 9. 100 and 30 for a normally distributed population of observations. Suppose you randomly selected from this population a sample of

9. Given: 9. μ 100 and σ 30 for a normally distributed population of observations. Suppose you randomly selected from this population a sample of size 36.

(a) Calculate the standard error of the mean.

(b) What is the probability that the sample mean will fall above 92?

(c) What is the probability that the sample mean will fall more than 8 points above the population mean of 100?

(d) What is the probability that the sample mean will differ from the population mean by 4 points or more (in either direction)?

(e) What sample mean has such a high value that the probability is .01 of obtaining one as high or higher?

(f) Within what limits would the central 95% of all possible sample means fall?