Question 3: Savings Rates

A study randomly selected 676 Canadians and asked them what portion of their income they allocate to savings/investments. The average found was 28%. Suppose the population mean is 24.8% and the standard deviation is 3.2%.

a. Determine the parameter, estimator, and estimate. What is the distribution of the estimator?

b. What is the probability that the estimate is greater than 26%?

c. What is the probability that the estimate is between 20% and 30%?

d. What sample size would be needed if the researchers want the standard deviation of the estimator to be less than or equal to 0.01% ?