Problem5 The mean CPU time for a class of programs on a certain mainframe comput

Question

Problem5 The mean CPU time for a class of programs on a certain mainframe computer is 2.52 minutes and the standard deviation is 0.37 minutes. Assume normality for the CPU time. (a) What is the probability that a randomly selected program will require between 2 and 3 minutes of CPU time? time a program will be considered as super-fast. considered super-slow? (b) Two and a half (2 ½) percent of the programs are found to be super-fast. Below what CPU (c) About 0.2% of the programs are found to be super-slow. Above what time a program will be

Explanation / Answer

mean is 2.52 and standard deviation is 0.37

a) P(2<x<3)=P((2-2.52)/0.37<z<(3-2.52)/0.37)=P(-1.41<z<1.3)=P(z<1.3)-(1-P(z<1.41))=0.9032-(1-0.9207)=0.8239

b) for top 2.5% we need to look at the value from the left of the curve for 1-0.025 i.e at 0.975 which is z=1.96

thus answer is 2.52+1.96*0.37=3.245

c) z for 0.2% value from left of curve is -2.88

thus answer is 2.52-2.88*0.37=1.4544

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