The number of messages that arrive at a web site is a poisson distributed random variable with a mean of 6 messages per hour. round your answers to four decimal places (e. g. 98.7654). (a) what is the probability that 5 messages are received in 1 hour? (b) what is the probability that 10 messages are received in 1.5 hours? (c) what is the probability that less than 2 messages are received in 1/2 hour?

a) There is a 16.0623% probability that 5 messages are received in 1 hour.

b) There is a 11.5880% probability that 10 messages are received in 1.5 hours.

c) There is a 22.4042% probability that 2 messages are received in 0.5 hours.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

is the Euler number

is the mean in the given time interval.

In this problem, we have a mean of 6 messages per hour.

(a) What is the probability that 5 messages are received in 1 hour?

Find the value of P when and

So

There is a 16.0623% probability that 5 messages are received in 1 hour.

(b) What is the probability that 10 messages are received in 1.5 hours?

The mean is 6 messages in one hour.

For 1.5 hours, the mean is 6*1.5 = 9 messages.

So

We have to find the value of P when and .

There is a 11.5880% probability that 10 messages are received in 1.5 hours.

(c) What is the probability that less than 2 messages are received in 1/2 hour?

The mean is 6 messages in one hour.

For 0.5 hours, the mean is 6*0.5 = 3 messages.

So

We have to find the value of P when and .

There is a 22.4042% probability that 2 messages are received in 0.5 hours.

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step-by-step explanation:

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.