Question

# A contractor is planning the acquisition of construction equipment, including bulldozers, needed for a new project...

A contractor is planning the acquisition of construction equipment, including

bulldozers, needed for a new project in a remote area. Suppose that from his prior

experience with similar bulldozers, he estimated that there is a 75% chance that

each bulldozer can remain operational for at least 6 month If he purchased three

bulldozers for the new project, after 6 months into the project please calculate the

probability using the binomial distribution that:

a. none of the bulldozers will be oper

ational?

b. all the bulldozers will be operational?

c. at least one bulldozer will be operational?

d. there will be only 1 bulldozer left operational?

e. only two bulldozers will be operational?

 here this is binomial with parameter n=3 and p=0.75

a)

none of the bulldozers will be operational P(X=0)=(3C0)*(0.75)0(1-0.75)3 =0.0156

b)all the bulldozers will be operational =P(X=3)=(3C3)*(0.75)3(1-0.75)0 =0.4219

c)

at least one bulldozer will be operational =1-P(none operational )=1-0.0156 =0.9844

d)

there will be only 1 bulldozer left operational =P(X=1)=(3C1)*(0.75)1(1-0.75)2 =0.1406

e) only two bulldozers will be operational =P(X=2)=(3C2)*(0.75)2(1-0.75)1 =0.4219

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