Suppose a worker needs to process 100 items. the time to process each item is exponentially distributed with a mean of 1 minute, and the processing times are independent. approximately, what is the probability that the worker finishes in less than 2.25 hours?

0.0368

Step-by-step explanation:

The cumulative distribution function for exponential distribution is :-

, where is the mean of the distribution.

Given : The time to process each item is exponentially distributed with a mean of 1 minute .

In hour, the mean time to process each item = hour

Then , the probability that the worker finishes in less than 2.25 hours :-

Hence, the probability that the worker finishes in less than 2.25 hours = 0.0368

the answer is d. 75%