Suppose that the distribution of retirement age in Canada is negatively skewed. The distribution has a mean of 65 and a variance of 16. (a) For a random sample of n = 81 retired Canadians, what is the probability that the average age of retirement in the sample is less than 64.5? (b) For a random sample of n = 81 retired Canadians, what is the probability that the average age of retirement in the sample is between 65 and 66?  (c) At what age would have at least 90% of the individuals in the sample retired? In other words, what is the 90th percentile for a random sample of n = 81 retired Canadians?

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Suppose that the distribution of retirement age in Canada is negatively skewed. The distribution has a mean of 65 and a variance of 16.

(a) For a random sample of n = 81 retired Canadians, what is the probability that the average age of retirement in the sample is less than 64.5?

(b) For a random sample of n = 81 retired Canadians, what is the probability that the average age of retirement in the sample is between 65 and 66? 

(c) At what age would have at least 90% of the individuals in the sample retired? In other words, what is the 90th percentile for a random sample of n = 81 retired Canadians?

(d) Everything else being equal, how would an increase in sample size affect the standard error of the mean? 

(e) Everything else being equal, how would an increase in sample size influence σ?

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