Question

1% of the checks received by an oil company is returned due to insufficient funds. Yesterday 450 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 one or more checks are returned. P(x>1)=

Answer 1

Solution:-) . X equals the number of these checks which will be returned due to insufficient funds out of 450. X ~ Bin (650,p) where, p = 1% = 0.01. Using Poisson distribution the parameter will be

$\lambda = np = 450 *0.01=4.5$

$P(X>1) = 1-P(X<1) = 1-P(X=0) 1- e^{-4.5} = 0.988891$

98.88% probability that one or more checks are returned.