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:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
mean of 10 minutes.
This means that [tex]m = 10[/tex], so [tex]\mu = \frac{1}{10} = 0.1[/tex]
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.
[tex]P(X \leq x) = 1 - e^{-0.1*6} = 0.4512[/tex]
45.12% probability a student waits less than 6 minutes.
