Math 323 Homework Solutions: Probability Distributions and Confidence Intervals, Assignments of Probability and Statistics

Download Math 323 Homework Solutions: Probability Distributions and Confidence Intervals and more Assignments Probability and Statistics in PDF only on Docsity! Math 323 Homework # 11 6.1. b) x̄ = 1.6633, s2 = .228097 use calculator c) Use Tchebysheff inequality P (|X − µ| < kσ) ≥ 1− 1 k2 = .75 1 k2 = .25, k = 2 k ± 2σ ≈ x̄± 2s = 1.6633± 2 √ .228097 = (.7081, 2.6185) 6.16. µ = 4, σ = .8 a) P (1 < x̄ < 5) = P ( 1− 4 .8/ √ 30 < Z < 5− 4 .8/ √ 30 ) = P (−20.54 < Z < 6.85) = 1 b) P (X1 + · · ·+X30 < 115) = P ( x̄ < 115 30 ) = P ( Z < 115 30 − 4 .8/ √ 30 ) = P (Z < −1.14) = .5− .3729 = .1271 6.24. midian=33 Let X be the # of people in the sample younger than 33. Then, X is binomial with p = .5 and n = 100. µ = 100× .5 = 50, σ = √ 100× .5× .5 = 5 µ± 2σ = 50± 10 = (40, 60) in (0, 100) 1