Suppose a simple random sample of size nequals48 is obtained from a population with muequals62 and sigmaequals14.
​(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 overbar.
​(b) Assuming the normal model can be​ used, determine ​P(x overbarless than65.5​).
​(c) Assuming the normal model can be​ used, determine ​P(x overbargreater than or equals64.3​).