The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2.5 minutes. (a) Find the probability that a customer has to wait more than 4 minutes. (Round your answer to three decimal places.) (b) Find the probability that a customer is served within the first minute. (Round your answer to three decimal places.) (c) The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use

a) 0.202 = 20.2% probability that a customer has to wait more than 4 minutes.

b) 0.33 = 33% probability that a customer is served within the first minute.

c) 11.5 minutes.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

In which is the decay parameter.

The probability that x is lower or equal to a is given by:

Which has the following solution:

The probability of finding a value higher than x is:

In this question:

(a) Find the probability that a customer has to wait more than 4 minutes.

0.202 = 20.2% probability that a customer has to wait more than 4 minutes.

(b) Find the probability that a customer is served within the first minute.

0.33 = 33% probability that a customer is served within the first minute.

(c) The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use

We have to find x for which:

So

Then

So 11.5 minutes.