The number of messages arriving at a multiplexer is a poisson random variable with mean 15 messages/second. use the central limit theorem to estimate the probability that more than 950 message arrive in one minute.

0.048 is the probability that more than 950 message arrive in one minute.

Step-by-step explanation:

We are given the following information in the question:

The number of messages arriving at a multiplexer is a Poisson random variable with mean 15 messages/second.

Let X be the number of messages arriving at a multiplexer.

Mean = 15

For poison distribution,

Mean = Variance = 15

From central limit theorem, we have:

where n is the sample size.

Here, n = 1 minute = 60 seconds

P(x > 950)

Calculation the value from standard normal z table, we have,  

0.048 is the probability that more than 950 message arrive in one minute.

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step-by-step explanation: