Question: This question has three parts.

1. Consider a large population with defect ratio of 1%. We draw a large number of samples, each of size 25 and count the number of defective items in each sample. Let Di denote the number of defective items found in sample i, i = 1, 2, . . . N, where N ≫ 1. Estimate the median, first quartile and third quartile of the sequence D1 , D2 , . . . , DN .
2. Let X ∼ N(μ = 2, σ2 = 0.04). Consider a large number of observations of X, that give the values x1 , . . . , xN , where N ≫ 1. Estimate the 12th percentile of the observations.
3. Consider the Fibonacci sequence given by the recurrence relation Fn = Fn −1 + Fn−2 , F(0) = F(1) = 1. Write the Fibonacci sequence up to n = 15. What percentile of the set of numbers you wrote is the number 21?

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