III. HOME WORK PROBLEMS

10. SAMPLE SIZE

This is a problem of determining how "representative" is 1,000 samples in capturing an arbitrary distribution.
  1. What is the probability that none of the 1,000 samples lie in the top-1% of the population?

  2. What is the probability that at least n (< 20) of the 1,000 samples lie in the top-1% of the population (you expect on the average 10 samples will lie in the top-1%)?

SOLUTION:
  1. The probability = (1 - 0.01)1000
  2. Prob(n >= 1) = 1 - (1 - 0.01)1000
    Prob(n >= 2) = 1 - (1 - 0.01)1000 - 1000C1 (0.99)999 (0.01)
    Prob(n >= 3) = 1 - (1 - 0.01)1000 - 1000C1 (0.99)999 (0.01) - 1000C2 (0.99)998 (0.01)2
    and so forth .


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