A simple random sample of size n equals=3737 is obtained from a population with μ equals=6969 and σ equals=1515.

​(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample​ mean? Assuming that this condition is​ true, describe the sampling distribution of x bar

​(b) Assuming the normal model can be​ used, determine
​P(x bar < 73.3​).

​(c) Assuming the normal model can be​ used, determine ​P(x bar ≥ 70.3​).