Students arrive at a library reference desk at an average ra

Students arrive at a library reference desk at an average rate of 15 per hour. Assume Poisson arrivals. What is the probability that NO MORE THAN 2 students arrive in 30 minutes?

Solution

mean for one hour = 15/hour

mean for 30 min = 15/2 = 7.5 student/30 min

lamda = 7.5

P(x=r) = e^(-lamda) * lamda^r / r!

P(x<2) = P(x=0) + P(x=1)

P(x<2) = e^(-7.5) * 7.5^0 / 0! + e^(-7.5) * 7.5^1 / 1!

P(x<2) = 0.004701