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
