Question

Highlight Rotate Markup Question 6 The total rain fall in Milwaukee for the Spring season is normally distributed with mean of 37 inches with a standard deviation of 5 inches (i.e. u=37 and =5). Given this information, determine: a) Probability of a total rain fall above 34 inches. b) Probability of a total rain fall between 36 and 40 inches. c) Probability of a total rain fall below 30 inches. c) Find the 85th percentile of the total rainfall. Tous Next wipoo

Answer 1

The total sain fall in mail wukee for the spring season is normally diBbwiloubed with mean of 37 incher with a standard deration of 5 inches l.e. X N N(4 E37 6=5) Probability PCX >34) of = a toteel rain fall above 34 incher is, 1 - P(x=34) "Z NNCO = 1- P(Z = -0.6) = 1 - 0.274253 - = 0.725747 ... PCX >34 = 0.72575 1 Probability of a total sain fall between 36 and 40 inches is, P( 36 < x <40) = p ( 36-37 LX-4 < 40-37) = P(-0.2 K Z L0.6) = P(Z 2016) - P(Z <-0.2) 0.725747 -0.420740 = 0.305007 [PC364 x 240) = 0.30501

Bobability of a total rain fall below 30 inches is P(X <30) = P/xy 30-37) = p (z 2 - 2 = P(Z < -1.4) = 0.080757 PCX <30) = 0.08076 The 85th percentile of the total reinfall is ine. PCX & x) = 0.85 1. P( x2x) = 0.85 P(x - x-37) - 0.85 p( 2 L x-37) = 0.85 a f(x-37) - 0.85 2-37 - F 960-85) 2-37 = 1.03643 2NN(O) 5 = x-37 = 1.03643 x 5 7 x 37 = 5.18215 > x = 5.18 215 + 37 x = 42.18215 [x = 42.182 x-37 5 ΠΟΙΟΙ of the total rainfall The is 85th percentile 42. 182