Determine whether the statement makes sense(or is clearlytrue) or does not make sense(or is clearlyfalse). Explain clearly.

A process consists of repeating thisoperation: Randomly select two values from a normally distributed population and then find the mean of the two values.

A.

The statement does not make sense. The Central Limit Theorem only guarantees that the distribution of sample means is approximately normal for suitably large sample sizes.

B.

The statement does not make sense. Since only two values are beingsampled, the distribution of sample means will take on a triangleshape, which is certainly not normal.

C.

The statement makes sense. The Central Limit Theorem guarantees that the distribution of sample means is approximately normal for suitably small sample sizes.

D.

The statement makes sense. Since the population is normallydistributed, the distribution of sample means will also be normallydistributed, regardless of sample size.

Determine whether the following data set is likely to be normally distributed. Explain the reasoning.

The measured systolic blood pressure of randomly selected adult females.

A.

Notnormallydistributed.Systolicbloodpressureswillbeaboutthesame for each person, causing a flat distribution curve characteristic of a uniform distribution.

B.

Normally distributed because any large data set yields normally distributed values.

C.

Not normally distributed. Most people will have pressures above the average causing a peak in the distribution at the right. nothing

D.

Normallydistributed.Systolicbloodpressurelevelsvaryaboveandbelowthe mean by similar amounts. The distribution has one peak and is symmetric. Systolic blood pressure results from many factors.