Question

he average time between accidents in a factory is 3 weeks. Find the probability that more than 5 weeks pass between accidents.

Answer 1

Solution :

Given that ,

mean = = 3

Using Poisson probability formula,

P(X = x) = (e^- * ^x ) / x!

Find P(X > 5)

P(X > 5) = 1 - P(X 5)

= 1 -  { P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) }

= 1 - { (e^-3 * 3⁰⁾ / 0! + (e^-3 * 3¹⁾ / 1! + (e^-3 * 3²⁾ / 2! + (e^-3 * 3³⁾ / 3! + (e^-3 * 3⁴⁾ / 4! + (e^-3 * 3⁵⁾ / 5! }

= 1 - { 0.0498 + 0.1494 + 0.224 + 0.224 + 0.168 + 0.1008 }

= 0.0839