lab3f09_ans

# lab3f09_ans - Problem 1 Normal approximation to Binomial n=...

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Unformatted text preview: Problem 1. Normal approximation to Binomial n= 100, p = .085, X = number of unemployed people (a) Verify that the conditions for using the Normal to approximation to the Binomial are satisfied. np = 8 . 5 > 5 and n (1- p ) = 91 . 5 > 5 Yes, the conditions are met. (b)Use Normal approximation to the Binomial to find the probability ¯ X = np = 100 * . 085 = 8.5 S = radicalBig np (1- p ) = 2.789 (i) P ( X ≥ 10) P ( X ≥ 10) = 1- P parenleftbigg Z ≤ 9 . 5- 8 . 5 2 . 789 parenrightbigg = 1- P ( Z ≤ . 36) = 0.36 (ii) P ( X ≤ 5) P ( X ≤ 5) = P ( X ≤ 5 . 5- 8 . 5 2 . 789 ) = P ( Z ≤ - 1 . 08) = 0.14 (iii) P ( X = 8) P ( X = 8) = P (7 . 5 < X < 8 . 5) = P parenleftbigg 7 . 5- 8 . 5 2 . 789 < Z < 8 . 5- 8 . 5 2 . 789 parenrightbigg = P (0 . 35855 < Z < 0) = . 5- . 3504 = .1496 1 (c) Calculate the exact answer to part (b)iii using the Binomial Probability Function P ( X = 8) = parenleftBigg 100 8 parenrightBigg * . 085 8 * (1- . 085) 92 = 0 . 14316 The result is a little smaller than in b(iii) because we are doing the exact calculation here.The result is a little smaller than in b(iii) because we are doing the exact calculation here....
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lab3f09_ans - Problem 1 Normal approximation to Binomial n=...

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