Answer: 0.99822
Step-by-step explanation:
Our inter-arrival time follows Poisson distribution with parameter 14 which is in hour so first we have to calculate this in minutes as we have to calculate probability in minutes.
So converting 14 into minutes will give =0.233
Let X=inter-arrival time between two customers
and here = 0.233
Probability(X is less than or equal to 2 minutes) = P(X=0) + P(X=1) + P(X=2)
Now the Poisson distribution has PDF =
So P(X = 0) = = 0.79215
P(X= 1) = = 0.18457
P(X=2) = = 0.02150
Now adding all three probability gives = 0.79215 +0.18457 + 0.02150=0.99822