Question

1. A fast-food restaurant manager knows that cars arrive at the drive-through at the rate of 3 cars per minute between the hours of 12 noon and 12.30 pm. The manger wants to determine and interpret the probability of following events;

1. Exactly 6 cars arrive between 12 noon and 12.05 pm.
2. Fewer than 6 cars arrive between 12.00 noon and 12.05 pm.
3. At least 6 cars arrive between 12 noon and 12.05 pm.

Answer 1

Let X is a random variable shows the number of cars arrive within 5 minutes. Here X has Poisson distribution with parameter . The pdf of X is

一15 1 51 P(X =x) =-1'

(a)

The probability that exactly 6 cars arrive between 12 noon and 12.05 pm is

P(X = 6) = e-15156 0.00484

(b)

The probability that fewer than 6 cars arrive between 12 noon and 12.05 pm is

(c)

The probability that at least 6 cars arrive between 12 noon and 12.05 pm is

e-1515" r! 1-0.00279 = 0.99721