*14. Suppose for a normally distributed population of observations you know that s 15, but you...

*14. Suppose for a normally distributed population of observations you know that s ¼ 15, but you don’t know the value of m. You plan to select a random sample (n ¼ 50) and use the sample mean to estimate the population mean.

(a) Calculate sX.

(b) What is the probability that the sample mean will fall within 5 points (in either direction) of the unknown value of m?

212 Chapter 10 Sampling Distributions

(c) What is the probability that the sample mean will fall within 2 points of m (in either direction)?

(d) The probability is .95 that the sample mean will fall within ______ points of m (in either direction).