1During the period of time that a local university takes pho

1.During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.

a.What is the expected number of calls in one hour?

b.What is the probability of three calls in five minutes?

c.What is the probability of no calls in a five-minute period?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
calls come in at the rate of one every two minutes.
a)
Per hour the rate is = 60 / 2 = 30 calls
b)
Per 5 mins the rate = 5/2 = 2.5

P( X = 3 ) = e ^-2.5 * 2.5^3 / 3! = 0.2138

c)
P( X = 0 ) = e ^-2.5 * 2.5^0 / 0! = 0.0821