(a) How can we calculate the probability that a random sample has a mean that falls within a given interval if the theoretical sampling distribution of the mean is normal or approximately normal? How is this di?erent from the process of ?nding the probability that a normally dis- tributed random variable assumes a value within a given interval?
(b) Draw a normal curve in the X- and z scales and show the percentage of the area under the curve within 1, 2, and 3 standard deviation units of its mean.