The number of hits on a certain website during a one-minute interval follows a Poisson distribution with a mean rate of four hits per minute. What is the probability that there is at least one hit in a 30-second period (that is the probability of one or more hits)

86.47% probability that there is at least one hit in a 30-second period

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

e = 2.71828 is the Euler number

is the mean in the given interval.

Mean rate of four hits per minute.

This means that , in which n is the number of minutes.

What is the probability that there is at least one hit in a 30-second period

30 seconds is 0.5 minutes, so

Either the site doesn't get a hit during this period, or it does. The sum of the probabilities of these events is 1. So

We want

Then

In which

86.47% probability that there is at least one hit in a 30-second period

true

explanation:

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: