Question

16). Please note that for every individually lettered problem from Chapter Six that appears on the exam, I am going to expect you to draw an appropriate The mean one-way commute to work in Knight Town is 13 minutes. The standard deviation is 2.6 minutes, and the population is normally distributed. What is the probability of randomly selecting one commute time and finding that: a). P (X< 12 mins) b). P (12<x< 17 mins) c). P (10<x< 12 mins) d). P (X> 17 mins) e). P (X > 10 mins) f). P (X< 17 mins) 1

Answer 1

Let x denote the Güven X-13 2.6 commute time xn Normal (10=13, 8 = 2.6) P(x< 12) PC < 12-13) = P(Z <-0.3846) 22 X-13 uN(o,) :(-0.38) 31 - $(0.38) standard P(x412) [using normal table = 1 -0.6490273 -0.351 9727

P =0.9382198- =0.9382198-0.3519727 -0.5862471 2.6 p(12<x<17) 12-13 < 8-13 ( 17 -13) P(-0.38 -0.3846 <2<1.5385) 23 X-13 u N(0,1) P(z<1.54) - P(Z <-0.38) $(1.54) - (-0.38) 20.9382198 - (1-(6-38)) - (1-0.6980273) .P/12 <x217) © Pl10 < X<12) - P( 1074 < t < P(-1.1538 << < -0.38461) P(Z <-0.38) - P(Z<-1-15) (-0.38) – (-1.15) = 0.3519721 – (1-5 (1.15)) = -0.3519721 - (1 -0.8749 281) P10 LXL12) @ P(x>17) 17-3) =P(2>1.53846) El-P(Z <1.54) =1-8 (1:54) - P 2 Р -0.3519721 - 0.1250719 20.2269002 P(x-13 > 2.6 2.6 21-0.9382198 -0.06 (7802 10-13 2.6 P(x>17) P(x310) = P(x-13 = P(Z) -1,1538) 1- P(Z <-1.45) = 1-3(-1.15) = 1 -(1-0.8749281) p(x>0) =0.8749281

다 F(x<l7) 1 - P(x>iz) =1 - o ok 17 902 20.939 28