Suppose that on average 1 person in 1000 makes a numerical e

Suppose that, on average, 1 person in 1000 makes a numerical
error in preparing his or her income tax return. If 10,000 returns are selected
at random and examined, find the probability that 6, 7, or 8 of them contain
an error.

Solution

Given X follows Poisson distribution with mean =10000/1000 = 10

P(X=x)=(10^x)*exp(-10)/x! for x=0,1,2,...

So the probability is

P(X=6) =(10^6)*exp(-10)/6! =0.06305546

P(X=7) = (10^7)*exp(-10)/7! =0.09007923

P(X=8)= (10^8)*exp(-10)/8! =0.112599