Question

The time between unplanned shutdowns of a power plant has an exponential distribution with a mean of 30 days. Find the probability that the time between two unplanned shutdowns is between 18 and 24 days.

Answer 1

Answer: 0.0995

Explanation:

The cumulative distribution function for exponential distribution for random variable x is given by :-

`F(x)=1-e^(-\lambda x)`, where
`\lambda` is the mean of the distribution .

Given : The time between unplanned shutdowns of a power plant has an exponential distribution with a mean of 30 days.

Then
`\lambda=(1)/(30)`

`P(x<18)=1-e^{-(1)/(30)*18}\approx0.4512`

`P(x<24)=1-e^{-(1)/(30)*24}\approx0.5507`

Now, the probability that the time between two unplanned shutdowns is between 18 and 24 days will be :-

`P(x<24)-P(x<18)=0.5507-0.4512=0.0995`

Hence, the probability that the time between two unplanned shutdowns is between 18 and 24 days =0.0995