Question

If an average of 12 customers is served per hour, what is the probability that the next customer will arrive in 9 minutes or less?

Answer 1

Solution :

Given that ,

mean = = 12

Using poisson probability formula,

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

P(X 9) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)

= (e^-12 * 12⁰⁾ / 0! + (e^-12 * 12⁰⁾ / 0! + (e^-12 * 12¹⁾ / 1! + (e^-12 * 12²⁾ / 2! + (e^-12 * 12³⁾ / 3! +(e^-12 * 12⁴⁾ / 4! + (e^-12 * 12⁵⁾ / 5! +(e^-12 * 12⁶⁾ / 6! + (e^-12 * 12⁷⁾ / 7! + (e^-12 * 12⁸⁾ / 8! + (e^-12 * 12⁹⁾ / 9!

= 0 + 0.0001 + 0.0004 + 0.0018 + 0.0053 + 0.0127 + 0.0255 + 0.0437 + 0.0655 + 0.0874

Probability = 0.2424

The probability that the next customer will arrive in 9 minutes or less is 0.2424