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.

A newspaper finds that the mean number of typographical errors per page is
six
six. Find the probability that​ (a) exactly
four
four typographical errors are found on a​ page, (b) at most
four
four typographical errors are found on a​ page, and​ (c) more than
four
four typographical errors are found on a page.

Answer 1

The applicable distribution is Poisson, since it relates to the number of successes/occurrences within a specified interval.

The probability of a given number, x, of occurrences is given by
P(x)=m^x*e^(-m)/x!
where m is the mean number of occurrences.

In the case of mean, m=6, the probability reduces to
P(x)=6^x*e^(-6)/x!

(a) x=4
P(4)=6^4*e^(-6)/4!=0.13385

(b) x<=4
P(X<=4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
=0.00248+0.01487+0.04462+0.08924+0.13385+0.28506
=0.28506

(c) x>4
P(X>4)=1-P(X<=4)
=1-0.28506
=0.71494