Question

Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. (Round your answers to four decimal places.)

Compute the probability of receiving two calls in a 5-minute interval of time.

Answer 1

The probability of receiving exactly two calls in a 5-minute interval, given a rate of 48 calls per hour, is calculated using the Poisson probability formula and is determined to be approximately 14.65%.

Step-by-step explanation:

To calculate the probability of receiving exactly two calls in a 5-minute interval at a reservation desk where calls arrive at the rate of 48 per hour, we can use the Poisson distribution formula, which is suitable for finding probabilities of a number of events happening in a fixed interval of time when these events occur with a known constant rate and independently of the time since the last event.

The formula for the Poisson probability is P(X=k) = (e-λ*λk)/k!, where λ is the average number of events in the interval, and k is the number of events for which we want to find the probability.

Here, λ for a 5-minute interval is (48 calls/hour) * (1 hour/60 minutes) * 5 minutes = 4 calls/5 minutes.

Thus, P(X=2) = e-4*42/2! = (0.0183)*16/2 = 0.1465 or 14.65%.