If the mean time between unscheduled maintenance of LCD displays in a hospital's CT scan facility is 4,000 operating hours,what is the probability of unscheduled maintenance in the next 5,000 hours?
A)0.8000
B)0.7135
C)0.2865
D)0.5000

Question

Quizplus · Accepted Answer

The mean time between unscheduled maintenance is 4,000 operating hours, which means the failure rate is (1/4000) per hour. To find the probability of unscheduled maintenance in the next 5,000 hours, we need to use the exponential distribution with the parameter lambda = 1/4000.

P(X < 5000) = 1 - e^(-lambda*X)
P(X < 5000) = 1 - e^(-1/4000 * 5000)
P(X < 5000) = 1 - e^(-1.25)
P(X < 5000) = 0.7135

Therefore, the probability of unscheduled maintenance in the next 5,000 hours is 0.7135, which corresponds to choice B.

If the Mean Time Between Unscheduled Maintenance of LCD Displays