Question

0) A retail store has implemented procedures aimed at reducing the number of bad checks cashed by its cashiers. The store's goal is to cash no more than eight bad checks per week. The average number of bad checks cashed is three per week a) Find the probability that the store's cashiers will not cash any bad checks in a particular week. b) Find the probability that the store will meet its goal during a particular week. c) During another particular week, the store has 6 bad checks cashed. Does this mean that the new procedures are not working? Explain.

Answer 1

Poisson's Distribution Formula:
P(X = x) = (e^-λ) (λ^x) / x!

Here, lambda = 3
a)
P(X = 0) = (e^-3) (3^0) / 0! = 0.0498

b)
P(X <= 8) = 0.9962
Excel function: =POISSON.DIST(8,3,TRUE)

c)
P(X > 6) = 1 - P(X <=6) = 0.0335
Excel function =1-POISSON.DIST(6,3,TRUE)

As the value of probability is less than 0.05, we can say new procedure is working