Suppose a simple random sample of size nequals 64 is obtained from a population with mu equals 74 and sigma equals 32 . ​(a) Describe the sampling distribution of x overbar . ​(b) What is Upper P left parenthesis x overbar greater than 78.6 right parenthesis ​? ​(c) What is Upper P left parenthesis x overbar less than or equals 64.2 right parenthesis ​? ​(d) What is Upper P left parenthesis 71.2 less than x overbar less than 81 right parenthesis​?
​(a) Choose the correct description of the shape of the sampling distribution of x overbar.
A. The distribution is skewed left.
B. The distribution is skewed right.
C. The distribution is approximately normal.
D. The distribution is uniform.
E. The shape of the distribution is unknown.