Question

Five road graders are used in the construction of a highway project. The operation life Tof each grader is a lognormal random variable with a mean life of 1500 hours and a CV of 30%. Assuming statistical independence among the conditions of the machines, what is the probability that there will be no more than two machines malfunctioning within 900 hours. [20 points] 5.

Answer 1

5)

We are given $\frac{\sigma}{\overline{x}}=0.3$

σ = 0.3(1500) = 450

So,

E(T) = 1500, S.D.(T) = 450

Now,

900 1500 P(T < 900) = P(Z < )-P(Z <-1.33) P(Z > 1.33) 450

1-P(Z < 1.33) = 1-0.90824-0.09176

Let Y denote the number of machines that malfunction within 900 hours. Then,

y ~ Bin(n 5、p= 0.09176)

y)-Ί ) (0.09 176)"(1-0.09 176)5-у. У-0, 1. 2. 3.4.5 Ply

Required probability =

(0) (0.09 176)0(1 Ply < 2)-P(y-0)-P(y = 1) + P(y-2)- 615-1 0.09 1705-0+ , ) (0.09 1701 (1-0.09 1705_1+(: ) (0.09176)2(1-0.09176)5-2ー 0,99330