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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 :

JeanaShupp

Answer: 0.0368

Step-by-step explanation:

The cumulative distribution function for exponential distribution is :-

[tex]P(x)=1-e^{-\lambda x}[/tex]

, where [tex]\lambda[/tex] 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 = [tex]\lambda=\dfrac{1}{60}[/tex] hour

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

[tex]P(x<2.25)=1-e^{-\frac{1}{60} \times2.25}\\\\\approx1-0.9632=0.0368[/tex]

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

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