Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities. The mean number of births per minute in a country in a recent year was aboutthreethree.Find the probability that the number of births in any given minute is​ (a) exactlyfourfour​,​(b) at leastfourfour​,and​ (c) more thanfourfour.

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Asked Feb 25, 2020
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Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities.
 
The mean number of births per minute in a country in a recent year was about
threethree.
Find the probability that the number of births in any given minute is​ (a) exactly
fourfour​,
​(b) at least
fourfour​,
and​ (c) more than
fourfour.
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Expert Answer

Step 1

The Poisson distribution:

A discrete random variable X is said to have a Poisson distribution with parameter λ then the probability mass function (pmf) of the random variable is given by:

Statistics homework question answer, step 1, image 1

Step 2

Calculation:

Here, lamda = 3.

a.

The probability that the number of births in any given minutes is exactly 4 is calculated as follows

Statistics homework question answer, step 2, image 1

Step 3

b.

The probability that the number of births in any given minutes is at least 4 is calculated as follows:

Statistics homework question answer, step 3, image 1

...

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