Exercise 2

Statistics Canada performed research on new houses sold in January 2021, in Toronto. The research findings are: median sales price was CAN 1,025,500 and the mean sales price was CAN 1,190,310.

• If you select samples of n=4, describe the shape of the sampling distribution of sample means
• If you select samples of n=100, describe the shape of the sampling distribution of sample means
• If you select a random sample of n=100, what is the probability that the sample mean will be less than CAN 1,000,000?
• The probability is 60% that the sample mean will be between what two values symmetrically distributed around the population mean?

Assume the standard deviation of the prices is CAN 580,250. present answers with 5 decimals.

Exercise 3

At a call center in India, for a population of 7 workers, the following data recorded represent the number of complaint days during the summer time in the year 2020:

7 9 12 15 21 30 36

a) if you sample without replacement, construct the sampling distribution of the mean for all possible samples of size n=2. Compute and compare the mean of all possible sample means and the population mean. Are they equal? What is this property called?

b) (repeat a) for all possible samples of size n=3

c) compare the shape of the sampling distribution of the mean in a) and b).

d) If you sample with replacement, repeat a), e.g.: construct the sampling distribution of the mean for all possible samples of size n=2. Compute and compare the mean of all possible sample means and the population mean.

present answers with 2 decimals.

Exercise 4

Uncle Jeremy goes to Las Vegas where he plays the following game: "

a player rolls a pair of dice. If, on any turn, the sum is under 7 (under 7 but not equal to 7), the player gets financially examined. Otherwise, she avoids financial examination". Suppose a player takes 5 turns at rolling the dice. Compute and present answers with 6 decimals):

• The probability that the player is financially examined no more than 2 times
• The probability that the player is financially examined more than 3 times
• The variance of the number of times the player is financially examined