The expected project completion time for the construction of a pressure vessel i

Question

The expected project completion time for the construction of a pressure vessel is 18 months and the project variance is 7. (Note: when using the Z tables- round your Z values to two decimal places before getting the probabilities from the tables. DO NOT round standard deviations prior to calculating Z values) NOTE: Enter probabilities as decimals (i.e. 92.31% should be entered as 0.9231) a) What is the probability that the project will require at least 19 months? b) What is the probability that the project will be completed within 24 months? c) What is the probability that the project will require at least 21 months? d) What is the probability that the project will be completed within 15 months? e) What is the probability that the project will take between 16 and 24 months to complete?

Explanation / Answer

Mean is 18 and variance is 7 thus standard deviation is sqrt(7)=2.65

a) P(x>19)=P(z>(19-18)/2.65)=P(z>0.38)=1-P(z<0.38), from the normal distribution table we get 1-0.6480=0.352

b) P(x<24)=P(z<(24-18)/2.65)=P(z<2.26), from normal table we get 0.9881

c) P(x>21)=P(z>(21-18)/2.65)=P(z>1.13)=1-P(z<1.13)=1-0.8708=0.1292

d) P(x<15)=P(z<(15-18)/2.65)=P(z<-1.13)=1-P(z<1.13)=0.1292

e) P(16<x<24)=P((16-18)/2.65<z<(24-18)/2.65)=P(-0.75<z<2.26)=P(z<2.26)-(1-P(z<0.75))=0.9881-(1-0.7734) =0.7615

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