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