Question

11. You manage a call center and your job is to make sure the employees aren’t slacking off when they are on the clock. You notice that one employee goes 20 minutes without picking up the phone, and you know the expected time between calls is 2 minutes. Derive an upper bound for the probability that the employee didn’t receive a call during the 20 minutes.

12. Suppose average weight in a city is 185 pounds. Suppose that John randomly selects 100 citizens, asks their weight, and averages the 100 numbers. Suppose that Julia does the same thing, only she asks 1,000 citizens instead of 100. Explain precisely, in a paragraph or so, what the Law of Large Numbers would tell you to expect about the average weights that Julia and John will calculate from their respective samples.

Answer 1

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11.

expecte time = 2 min

rate of calls = 1/expected time = 1/2 calls/min

P(T>t) = e^(-rate * t)

P(T>20 min) = e^(-(1/2) * 20)

= 0.000045

12.

The law of large numbers, in probability and statistics, states that as a sample size grows, its mean gets closer to the average of the whole population.

therefore, here we would expect the average weight found by Julia would be closer to 185 punds (population mean) tha the average weight calculated by John.

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