A simple random sample of size nequals=1414 is obtained from a population with muμequals=6363 and sigmaσequals=1717. ​
(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 overbarx.
​(b) Assuming the normal model can be​ used, determine ​P(x overbarxless than<66.566.5​). ​
(c) Assuming the normal model can be​ used, determine ​P(x overbarxgreater than or equals≥64.164.1​).