Question

Suppose that average male weight in the US is 175 pounds with a standard deviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean x̄_n .

a) What does the law of large numbers tell you about x̄_n , the average of the 1,000? Be precise in your answer using about 1 to 3 sentences.

b) What is the variance of x̄_{n ?}

c) Use your answer to part (b), and Chebyshev’s inequality, to come up with a quantitative upper bound for the probability that x̄_n is more than a certain distance of 175. (Choose a distance you find illustrative).

Answer 1