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Chapter 8: Q. 8.16 (page 391)

A.J. has 20 jobs that she must do in sequence, with the times required to do each of these jobs being independent random variables with mean 50 minutes and standard deviation 10 minutes. M.J. has 20 jobs that he must do in sequence, with the times required to do each of these jobs

being independent random variables with mean 52 minutes and standard deviation 15 minutes.

(a) Find the probability that A.J. finishes in less than 900 minutes.

(b) Find the probability that M.J. finishes in less than 900 minutes.

(c) Find the probability that A.J. finishes before M.J.

Short Answer

Expert verified

PA.J.<900鈮�0.01267PM.J.<900鈮�0.01845PA.J.>M.J.鈮�0.4565

Step by step solution

01

Given information

The summary for A.J. is

n=20,饾渿1=50and饾湈1=10

The summary for M.J. is

m=20,饾渿2=52and饾湈2=15

02

Part (a)

PA.J.<900=PA.J.-20*501020<900-20*501020鈮�P(Z<-5)鈮�0.01267

03

Part (b)

PM.J.<900=PA.J.-20*521520<900-20*521520鈮�P(Z<-2.087)鈮�0.01845

04

Step (c)

P(A.J.>M.J.)=P(A.J.-M.J.>0)=P(A.J.-M.J.)-(饾渿1-饾渿2)饾湈12+饾湈22>-(饾渿1-饾渿2)饾湈12+饾湈22=PZ>-(50-52)102+152=PZ>2335鈬�P(A.J.>M.J.)鈮�0.4565

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