Question

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?

Answer 1

Answer: 0.0368

Step-by-step explanation:

The cumulative distribution function for exponential distribution is :-

$P(x)=1-e^{-\lambda x}$

, where $\lambda$ 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 = $\lambda=\dfrac{1}{60}$ hour

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

$P(x$

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