Question

Suppose a simple random sample of size

nequals=4444

is obtained from a population with

muμequals=6767

and

sigmaσequals=1414.

​(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 overbarx.

​(b) Assuming the normal model can be​ used, determine

​P(x overbarxless than<70.470.4​).

​(c) Assuming the normal model can be​ used, determine

​P(x overbarxgreater than or equals≥68.668.6​).

Click here to view the standard normal distribution table (page 1).

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Click here to view the standard normal distribution table (page 2).

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​(a) What must be true regarding the distribution of the​ population?

A.

The population must be normally distributed.The population must be normally distributed.

nothing

B.

The population must be normally distributed and the sample size must be large.

C.

There are no requirements on the shape of the distribution of the population.

D.

Since the sample size is large enough comma the population distribution does not nbspSince the sample size is large enough, the population distribution does not

need to be normal.

Answer 1

Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(1.6109, TRUE)" to find the probability.

Refer Standard normal table/Z-table to find the probability OR use excel formula "=NORM.S.DIST(0.7581, TRUE)" to find the probability.