Question

Suppose that incoming calls per hour to a customer service center at a small credit union are uniformly distributed between zero and six calls. The probability that fewer than three calls are received per hour is.

Answer 1

Since the incoming calls per hour to the customer service center are uniformly distributed between zero and six calls, the probability density function (PDF) is:

f(x) = 1/6, 0 ≤ x ≤ 6

where x is the number of calls per hour.

To find the probability that fewer than three calls are received per hour, we need to calculate the area under the PDF curve between zero and three calls:

P(X < 3) = ∫[0,3] f(x) dx

= ∫[0,3] (1/6) dx

= (1/6) * [x]_0^3

= (1/6) * (3 - 0)

= 1/2

Therefore, the probability that fewer than three calls are received per hour is 1/2 or 0.5.