Question

The computer that controls a bank's automatic teller machine crashes a mean of 0.5 times per day. What is the probability that, in any seven-day week, the computer will crash more than 5 times? Round your answer to four decimal places.

Answer 1

X ~ Poisson ()

Where = 0.5 per day

So for 7 days,   = 0.5 * 7 = 3.5

Poisson probability distribution is

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

So,

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^-3.5 + e^-3.5 * 3.5 + e^-3.5 * 3.5² / 2! + e^-3.5 * 3.5³ / 3! + e^-3.5 * 3.5⁴ / 4! + e^-3.5 * 3.5⁵ / 5! ]

= 1 - 0.8576

= 0.1424