Question

Customers arrive at a shopping mart randomly at a rate of 7 per hour.

a)     Find the probability that during any 90 minutes’ period, the number of customers arriving at the shopping mart is exactly 8.

b)     If a customer arrives at 11.30 am, find the probability that the next patient arrives before 11.45 am.

Answer 1

a

$\lambda$=7 per hour

in 90 mins $\lambda$=10.5 per hour

P(x)=$\frac{\lambda^x(e^-\lambda)}{x!}$

P(8)=$\frac{10.5^8\cdot e^-10.5}{8!}$

P(8)=0.1009

b

For 15 mins $\lambda$=7/4 per 15 mins

P(1)=$\frac{(7/4)^1\cdot e^-7/4}{1!}$

P(1)=0.3041