Question

The time to process orders at the service counter of a pharmacy store are exponentially distributed with mean 5 minutes. Suppose that 100 customers visit the counter in a day. Use CLT to estimate the following.

(1) What is the probability that the total service time of the 100 customers does not exceed 10 hours?

(2) What is the probability that at least half of the 100 customers need to wait more than 3.47 minutes? (Note: to simply the calculations, you could use the fact that 3.47 ≈ 5 ln 2)

Answer 1

Let X be the time to process orders at the service counter of a pharmacy store.

X~Exp(mean=5 minutes)

n=100

To find

Now

Let X be the number of customers who have to wait more than 3.47 minutes

Using binomial distribution

=

Answer is 0.5