lab3f09_ans

lab3f09_ans - Problem 1. Normal approximation to Binomial...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

Page1 / 4

lab3f09_ans - Problem 1. Normal approximation to Binomial...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online