Suppose a simple random sample of size

n=14

is obtained from a population with

=66

and

=19.

(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.

(b) Assuming the normal model can be used, determine

P(x<70.1).

(c) Assuming the normal model can be used, determine

P(x67.2).