Question

A time overrun is defined as the inability of a contractor to complete a construction project...

A time overrun is defined as the inability of a contractor to complete a construction project within the original contract time schedule. From past records, it has been observed that 15 out of every 100 state contracts in a certain state result in time overruns. Next year, the state intends to let out 10 construction contracts.

(a)      Find the probability that more than 2 of next year’s contracts will have a time overrun.

(b)     Find the probability that exactly 3 of next year’s contracts will have a time overrun.

(c)      How many time overrun contracts can the state expect next year?

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Answer #1

here this is binomial distribution with parameter n=10 and p=15/100 =0.15

a) probability that more than 2 of next year’s contracts will have a time overrun =P(X>2)

=1-P(X<=2) =1-(P(X=0)+P(X=1)+P(X=2))=1-10C0(0.15)0(0.85)10-10C1(0.15)1(0.85)9-10C2(0.15)0(0.85)8

=0.1798

b)

probability that exactly 3 of next year’s contracts will have a time overrun =10C3(0.15)3(0.85)7

=0.1298

c)

expected number =np=10*0.15 =1.5

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