Poisson distribution question. Help me please.?

Question

The number of typo errors in textbooks follow the Poisson distribution with a mean of 1.5 per 100 pages. A teacher selects 400 pages of the textbook, what is the probability that there are 4 or more typo errors ?

Answer 1

X ~ Poisson(λ)

the density function is:

P(X = x) = λ^x * exp(-λ) / x! for x = 0, 1, 2, 3, 4, ....
P(X = x) = 0 otherwise

The sum of independent Poisson random variables also have the Poisson distribution with a mean of the sum.

Let Y be the number of errors on 400 pages.

Y ~ Poisson(400 * 1.5/100) = Poisson(6.6)

P(Y ≥ 4) = .... well this could be an infinite sum or you can see that this is:

P( Y ≥ 4 ) = 1 - P(Y = 0) - P(Y =1) - P(Y = 2) - P(Y = 3)
= 1 - 0.001360368 - 0.008978429 - 0.029628816 - 0.065183395
= 0.894849

Answer 2

1.5 for 100
pages in book = 400
400 div by 100 = 4

4 * 1.5 = 6

HIGH probability greater than 4 errors