the number of messages that arrive at a web site is a possion distirbuted random variable with a mean of 5 messages per hour. ro

Question

2 years ago

8

und your asnwers to four decimal places. what is the probaiblity taht 5 messages are received in 1 hour

1 answer:

mylen [45] · Answer 1 · 2024-01-29T10:40:47+03:00

17.54% is the probability that 5 messages are received in 1 hour.

The chance that X reflects the number of successes of a random variable in a Poisson distribution is provided by the following formula:

P(X = x) = ( $e^{-u}$ × $u^{x}$ ) ÷ x!

In where x is the number of successes, e is the Euler number, and u is the mean in the specified time frame.

In this case, the average message rate is 5 messages per hour.

The probability of receiving 5 texts in one hour.

Determine the value of P for x = 5 and u = 6.

P(X = x) = ( $e^{-5}$ × $(5)^{5}$ ) ÷ 5!

P(X = x) = 21.0560 ÷ 5!

P(X = x) = 0.1754

There is a 17.54% chance that 5 messages will be received in 1 hour.

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