Question

After arriving at the university student medical clinic, the waiting times to receive service after checking-in follow an exponential distribution with a mean of 10 minutes.
How many students are served per hour?



Calculate the probability a student waits less than 6 minutes.

Answer 1

Answer:

6 students are served per hour.

45.12% probability a student waits less than 6 minutes.

Step-by-step explanation:

Exponential distribution:

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

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

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

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

mean of 10 minutes.

This means that $m = 10$, so $\mu = \frac{1}{10} = 0.1$

How many students are served per hour?

One student is served each 10 minutes, on average

An hour has 60 minutes

60/10 = 6

6 students are served per hour.

Calculate the probability a student waits less than 6 minutes.

$P(X \leq x) = 1 - e^{-0.1*6} = 0.4512$

45.12% probability a student waits less than 6 minutes.