Find the indicated probabilities using the geometric distribution, Poisson distribution, or the binomial distribution. The mean number of births per minute in a given country in a recent year was about 6. Find the probability that the number of births in any given minute is exactly five. Round to four decimal places as needed.

0.1606 = 16.06% probability that the number of births in any given minute is exactly five.

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.

In this question:

We only have the mean during an interval, and this is why we use the Poisson distribution.

The mean number of births per minute in a given country in a recent year was about 6.

This means that

Find the probability that the number of births in any given minute is exactly five.

This is P(X = 5). So

0.1606 = 16.06% probability that the number of births in any given minute is exactly five.

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