Exponential distribution

Question

The average time between accidents in a factory is 7 weeks.

Find the probability that more than 21 weeks pass between accidents.

Answer 1

The time between occurrences, x, is often modeled by the exponential cumulative distribution:

P(x>a) = exp(-a / θ)

where θ is both the population mean (mu) and the population standard deviation (sigma).

So,

P(x>21) = exp(-21/7) = exp(-3) = 0.050

a 5% probability of going more than 21 days without an accident when the mean time between them is 7 days.