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? Step 1 We need to find a so that P(X ≥ a) =

The number of minutes advertisement should use is found.

x ≅ 12 mins

Step-by-step explanation:

(MISSING PART OF THE QUESTION: AVERAGE WAITING TIME = 2.5 MINUTES)

For such problems, we can use probability density function, in which probability is found out by taking integral of a function across an interval.

Probability Density Function is given by:

Consider the second function:

Where Average waiting time = μ = 2.5

The function f(t) becomes

The manager wants to give free hamburgers to only 1% of her costumers, which means that probability of a costumer getting a free hamburger is 0.01

The probability that a costumer has to wait for more than x minutes is:

which is equal to 0.01

Solve the equation for x

Take natural log on both sides

The costumer has to wait x = 11.53 mins ≅ 12 mins to get a free hamburger

step-by-step explanation:

in which figure is point g a centroid