Suppose that phone calls to the President’s office at Lehman College arrive independently and at random, with outside calls arriving at an average rate of 3 in any 10 minute period, and inside calls at an average rate of 4 in any 10 minute period. Compute the probability that 2 or more calls arrive in any 2 minute period.

40.82% probability that 2 or more calls arrive in any 2 minute period.

Step-by-step explanation:

We have the mean during a time interval, so we use the poisson distribution to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

10 minutes.

3 outside calls, 4 inside. So mean of 3+4 = 7.

That is, 0.7 calls per minute.

Compute the probability that 2 or more calls arrive in any 2 minute period.

2 minutes, so

Either less than two calls arrive, or two or more do. The sum of the probabilities of these events is decimal 1. So

We want . So

In which

40.82% probability that 2 or more calls arrive in any 2 minute period.