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kolbaska11 [484]
2 years ago
13

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?
Mathematics
1 answer:
Hunter-Best [27]2 years ago
3 0

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

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