Solutions HWA4

11.14a:

mu_{SUM} = n*mu = 10*40 = 400 minutes

sigma_{SUM} = sqrt[n]*sigma = sqrt[10]*15 = 47.43 minutes

11.14b: 6 hours = 360 minutes.

Pr(SUM <= 360) = Pr(Z <= (360 – 400)/47.43) = Pr(Z < = -.8433) = normalcdf(-999999,360,400,sqrt[10]*15) = .1995

11.20a: Pr(IQ > 115) = Pr(IQ > 115.5) = normalcdf(115.5,9999999,100,15) = .1507

11.20b: (.1507)^2 = .0227

11.20c: .1507 + .1507 - .0227 = .2787 or 1 – (1- .1507)^2 = .2787

11.20d: Pr(X-bar > 115) = Pr(z > (115 – 100)/(15/sqrt[2])) = normalcdf(115,99999999,100,15/sqrt(2)) = .0786 (Here we do not use the continuity correction. If you do, then you get Pr(X-bar > 115) = Pr(SUM > 230) = Pr(SUM > 230.5) = .0752)

11.38a: Pr(P < .19) = Pr(K < 76) = Pr( < 75.5) = Pr(Z < (75.5 – 80)/sqrt[400*.20*.80]) = .2869

11.38b: Pr(SUM > 19,000,000) = Pr(Z > (19000000 – 18000000)/sqr[400]*25000) = .0228