An automated phone system can answer three calls in a five-minute period. Assume that calls occur at an average rate of 1.2 every five minutes and follow a Poisson probability distribution. Calculate the probability that no calls will occur during the next ten minutes.

The probability that no calls will occur during the next ten minutes is 0.0907.

Step-by-step explanation:

Poisson distribution:

Poisson distribution is a statistical distribution that helps to find out the number of events is likely occur in a specific time period.

Given that,

Calls occur at an average rate of 1.2 every 5 minutes.

The average rate of call is per minute.

Here,

, t=10 and x=0

                  =0.0907

The probability that no calls will occur during the next ten minutes is 0.0907.

1/2(2*4)=6 $$- agahajakanajak