Please show your work, thank you!

Which of the following are consequences of the Central LimitTheorem? I'm not sure why II and III are correct and the others arenot.

I) A SRS of resale house prices for 100 randomly selectedtransactions from all sale

transactions in 2001 (in Toronto) will be obtained. Since thesample is large, we

should expect the histogram for the sample to be nearlynormal.

II) We will draw a SRS (simple random sample) of 100students from all University

of Toronto students, and measure each person’scholesterol level. The average

cholesterol level for the sample should be approximatelynormally distributed.

III) We want to estimate the proportion of Ontariovoters who intend to vote for the

Liberal party in the next election, and decide to draw aSRS of 400 voters. The

percentage of the people in the sample who will say thatthey intend to vote

Liberal is approximately normallydistributed.

IV) We will draw a SRS of 100 adults from the Canadian military,and count the

number who have the AIDS virus. The number of individuals in thesample who

will be found to have the AIDS virus should be approximatelynormally

distributed.

V) We are interested in the average income for all Canadianfamilies for 2001. The

mean income for all Canadian families should be approximatelynormal, due to

the large number of families in the population.