A simple random sample of size nequals12 is obtained from a population with muequals64 and sigmaequals15.
​(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 overbar.
​(b) Assuming the normal model can be​ used, determine ​P(x overbarless than67.3​).
​(c) Assuming the normal model can be​ used, determine ​P(x overbargreater than or equals65.1​).
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Part 1
​(a) What must be true regarding the distribution of the​ population?
A.The population must be normally distributed. nothing
The population must be normally distributed. nothing
B.
The sampling distribution must be assumed to be normal.
C.
The population must be normally distributed and the sample size must be large.
D.Since the sample size is large enough comma the population distribution does not need to be normal.
Since the sample size is large enough comma the population distribution does not need to be normal.