A division within a transportation company is responsible for performing mainten

Question

A division within a transportation company is responsible for performing maintenance on the fleet of trucks used by a company. Trucks in need of repair arrive to the maintenance division according to a Poisson process having a rate of 0.27 trucks per hour. Suppose we begin observing the maintenance division at some point in time.

a) What is the probability that it is at least 1.5 hours until the first truck arrives?

b) On average how long would you expect it to be until the first truck arrives?

c) What is the expected time between thae arrival of the fifth truck and the sixth truck?

d) What is the standard deviation of the time until the first truck arrives?

e) What is the probability that the third truck arrives within 15 minutes of the second truck?

Explanation / Answer

Answer to part a)

x = 1

P(x=1) = (0.27)^1 * (e^-0.27) / 1!

P(x=1) = 0.27 * e^-0.27 = 0.27 * 0.7634

P(x=1) = 0.2061

.

Answer to part b)

the average time of arrival of one truck =

0.27 truck arrives in 1 hour

1 truck arrives in 1 /0.27 hours

1 truck arrives = 3.7037 hours

.

Answer to part c)

The interarrival time between any two trucks = 1/0.27 = 3.7037

.

Answer to part d)

We got lambda = 0.27

.

Standard deviation = sqrt(lambda)

Standard deviation = sqrt(0.27)

Standard deviation = 0.5196

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