Question

If arrivals follow a poisson distribution with mean 1.2 arrivals per minute, find the 75th percentile of waiting times until the next arrival (i.e., 75 percent below).

Answer 1

To solve this given problem, we make use of the formula:

e ^ (- μ x) = (1 – nth percentile)

where the variables are:

μ is the mean value or population mean = 1.2 arrivals per minute

x is the value at the nth percentile = unknown value

nth percentile = 75th percentile or 75%  = 0.75

 

Substituting all the given values into the equation to find for x:

 

e ^ (- 1.2 x) = 1 – 0.75

e ^ (- 1.2 x) = 0.25

 

Taking the ln of both sides:

- 1.2 x = ln 0.25

x = - (ln 0.25) / 1.2

x = 1.155

 

Therefore the 75th percentile is 1.155 arrivals per minute