Suppose a simple random sample of size n=48

is obtained from a population with =64

and =18

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? Assuming the normal model can be used, describe the sampling distribution

x overbarx.

(b) Assuming the normal model can be used, determine P(x overbarxless than<67.5).

(c) Assuming the normal model can be used, determine P(x overbarxgreater than or equals66.1).

suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean =168 days and standard deviation =12 days.

• What is the probability that a randomly selected pregnancy lasts less than 164 days?