Question

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

sixsix.

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.

Answer 1

Answer:

Given that,

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 six.

i.e

We will need to use Poisson distribution to compute the given probabilities

Find the probability that the number of births in any given minute is,

(a).

Exactly four:

The required probability =P(X=4)

We know that,

Poisson distribution is,

Here x=4 and .

=4163.7681/24

=173.4903375

=173.49(Approximately)

Therefore, the probability that the number of births in any given minute is exactly four is 173.49.

(b).

At least four:

=1-(0.238996)

=0.761004

=0.761 (Approximately)

Therefore, the probability that the number of births in any given minute is at least 4 is 0.76.

(c).

More than four:

=0.16064+0.16064

=0.32128

=0.32(Approximately)

Therefore, the probability that the number of births in any given minute is more than 4 is 0.32.