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Nitella [24]
2 years ago
14

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.
Mathematics
1 answer:
ExtremeBDS [4]2 years ago
8 0

Answer:

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:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu 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 \mu = 6

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

This is P(X = 5). So

P(X = 5) = \frac{e^{-6}*6^{5}}{(5)!} = 0.1606

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

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