Suppose a simple random sample of size n=13 is obtained from a population with =65 and =16.

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the samplemean? Assuming the normal model can beused, describe the sampling distribution x.

(b) Assuming the normal model can beused, determine P(x<68.4).

(c) Assuming the normal model can beused, determine P(x66.4).

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

A.

Sincethesamplesizeislargeenough,thepopulationdistributiondoesnot

needtobenormal.

B.

Thepopulationmustbenormallydistributed.

C.

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

D.

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

Assuming the normal model can beused, describe the sampling distribution x.

A.

Normal, with x=65 and x=16

13

B.

Normal, with x=65 and x=16

C.

Normal, with x=65 and x=13

16

(b) P(x<68.4)=

nothing

(Round to four decimal places asneeded.)

(c) P(x66.4)=

nothing

(Round to four decimal places asneeded.)