Question

The manager of the local grocery store has determined that, on the average, 4 customers use the service desk every half-hour. Assume that the number of customers using the service desk has a Poisson distribution. What is the probability that during a randomly selected half-hour period exactly 2 customers use the service desk?

1) .0183
2) .0733
3) .1465
4) .9084

Answer 1

The probability that exactly 2 customers use the service desk in a randomly selected half-hour period can be calculated using the Poisson distribution formula.

Step-by-step explanation:

To solve this problem, we can use the Poisson distribution formula. The formula for the probability of X successes in a given interval is: P(X = k) = (e^(-λ) * λ^k) / k!. In this case, λ (the average number of customers using the service desk) is 4. To find the probability that exactly 2 customers use the service desk in a randomly selected half-hour period, we substitute k = 2 into the formula:

P(X = 2) = (e^(-4) * 4^2) / 2!

P(X = 2) = (e^(-4) * 16) / 2

Using a calculator, we find that P(X = 2) is approximately 0.1464, which is closest to option 3) 0.1465.