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. Find the probability that​ (a) exactly five typographical errors are found on a​ page, (b) at most five typographical errors are found on a​ page, and​ (c) more than five typographical errors are found on a page.

Answer 1

A newspaper finds that the mean number of typographical errors per page is six. Let X be the number of typographical errors found on any given page. We can say that X has a Poisson distribution with mean 6 errors per page and parameter

The probability that X=x typographical errors are found on a​ page is

(a) the probability that​ exactly five typographical errors are found on a​ page is

An event is considered unusual of the probability of the event is less than 0.05. Here, the probability of this event is not less than 0.05

ans: the probability that​ exactly five typographical errors are found on a​ page is 0.1606. This event is not unusual as the probability is not less than 0.05

(b) the probability that at most five typographical errors are found on a​ page is

Note: using Ti-83, press 2nd+VARS select poissoncdf

enter this and get (first input is mean, the second input corresponds to X<=5)

An event is considered unusual of the probability of the event is less than 0.05. Here, the probability of this event is not less than 0.05

ans: the probability that​ at most five typographical errors are found on a​ page is 0.4457. This event is not unusual as the probability is not less than 0.05

(c) the probability that​ more than five typographical errors are found on a page is

ans: the probability that​ more than five typographical errors are found on a page is 0.5543. This event is not unusual as the probability is not less than 0.05