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 four typographical errors are found on a​ page, (b) at most four typographical errors are found on a​ page, and​ (c) more than four typographical errors are found on a page.

Answer 1

In this case, the Poisson distribution is the best one to use. The formula for Poisson distribution is given as:

P[x] = e^-m * m^x / x! 

Where,

m = mean number of typographical errors = 6

x = sample value

A. The probability of exactly 4 errors are found on a page is:

P[4] = e^(-6) * 6^4/4!

P[4] = 0.1339

B. The probability that at most 4 errors will be the summation of x = 0 to 4:

P[0] = e^(-6) * 6^0/0! = 2.479 E -3

P[1] = e^(-6) * 6^1/1! = 0.01487

P[2] = e^(-6) * 6^2/2! = 0.04462

P[3] = e^(-6) * 6^3/3! = 0.08924

 

Therefore summing up all including the P[4] in A gives:

P[at most 4] = 0.2851

 

C. The probability that more than 4 would be the complement of answer in B.

P[more than 4] = 1 - P[at most 4]

P[more than 4] = 1 - 0.2851

P[more than 4] = 0.7149