Question

Employees arrive at a cafeteria according to a Poisson process at an average rate of 30 employees per hour. The probability that after one employee arrives, the next one will arrive at least 3 minutes later is _________.

a. 0.223
b. 0.202
c. 0.183
d. 0.162
e. 0.143

Answer 1

a. 0.223

Step-by-step explanation:

Calculation for the Probability that after one employee arrives, the next one will arrive at least 3 minutes

Since no one comes in 3 minutes,hence:

3minutes/60 =1/20 hours

Thus, the Probability will be calculated as:

Probability=e^20/30

Probability=0.223

Therefore the Probability that after one employee arrives, the next one will arrive at least 3 minutes will be 0.223