Question

1% of the checks received by an oil company is returned due to insufficient funds. Yesterday 400 checks were received in the mail. Let x equals the number of these checks which will be returned due to insufficient funds. Use the Poisson distribution to compute the binomial probability that less than three checks are returned. P(x < 3) =

Answer 1

it is given that sample size n = 400 and probability p = 1% = 1/100 = 0.01

so, poisson distribution mean = n*p

= 400*0.01

= 4

So, mean = 4

P(x less than 3) = P(x=0) + P(x=1) + P(x+2)

using poission distribution formula

and

Adding all three probabilities

P(x less than 3) = 0.01832 + 0.07326 + 0.14653

= 0.2381