Suppose for a normally distributed population of observations you know that 14. σ 15, but you don't know the value of μ. You plan to select a random sample (n = 50) and use the sample mean to estimate the population mean.
(a) Calculate σX .
(b) What is the probability that the sample mean will fall within 5 points (in either direction) of the unknown value of μ?
(c) What is the probability that the sample mean will fall within 2 points of μ (in either direction)?
(d) The probability is .95 that the sample mean will fall within _____ points of μ (in either direction).