The number of failures of a testing instrument from contamin

The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a mean of 0.013 failure per hour.

(a) What is the probability that the instrument does not fail in an 8-hour shift?

(b) What is the probability of at least one failure in a 24-hour day?

Round your answers to four decimal places (e.g. 98.7654).

Solution

Solution:

0.013 failure per hour

a.

for 8-hr shift

mean = 0.013 * 8 = 0.104

P(x=0) = e^(-m) * m^0/0!

P(x=0) = e^(-0.104)

P(x=0) = 0.901225

Probability of zero failure = 90.1225 %

b.

for 24 hr shift,

mean = 0.013 * 24 = 0.312

P(x>=1) = 1 - P(x=0)

P(x>=1) = 1 - e^(-m) * m^0 / 0!

P(x>=1) = 1 - e^(-0.312)

P(x>=1) = 1 - 0.731981

P(x>=1) = 0.268018

So,

probability of atlrast one failure in 24 hr is 26.8018%