Question

Cars enter a car wash at a mean rate of 3 cars per half an hour. What is the probability that, in any hour, at least 3 cars will enter the car wash

Answer 1

0.938

Explanation:

Using the poisson probability relation:

P(x = x) = (e^-λ * λ^x) ÷ x!

λ = 3 per half an hour = 6 cars per hour

P(x ≥ 3) = 1 - [p(x = 0) + p(x = 1). + p(x = 2)]

P(x ≥ 3) = (e^-6* (6^0 + 6^1 + 6^2/2!))

P(x ≥ 3) = 1 - (e^-6 * (1 + 6 + 18)

P(x ≥ 3) = 1 - (e^-6 * 25)

P(x ≥ 3) = 1 - (0.0024787 * 25)

P(x ≥ 3) = 1 - 0.0619688

P(x ≥ 3) = 0.9380311

= 0.938