Question: A sample random sample of size n = 20 is obtained form a population with \[\mu =64\] and \[\sigma =17\].

(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 \[\bar{x}\].

(b) Assuming that the requirements described in part (a) are satisfied, determine \[P(\bar{x}<67.3)\]

(c) Assuming that the requirements described in part (a) are satisfied, determine \[P(\bar{x}\ge 65.2)\]