The probability that a customer will use a stolen credit card to make a purchase at a certain Target store is 0.003. If 400 purchases are made in a given day, what is the approximate Poisson probability that 4 or fewer will be with stolen cards?
A).0053
B).0076
C).9923
D).0555

Question

Quizplus · Accepted Answer

The Poisson probability formula is used here, given by P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the mean number of successes (λ = np), and k is the number of successes we're interested in. For this scenario, λ = 400 * 0.003 = 1.2. We're interested in the probability of 4 or fewer successes, which requires summing the probabilities for 0, 1, 2, 3, and 4 successes. This calculation is cumbersome by hand but is well approximated by Poisson probability tables or a calculator. The result is approximately 0.9923, indicating a high probability of 4 or fewer purchases with stolen cards.

The Probability That a Customer Will Use a Stolen Credit