Question

in a food processing and packaging plant, there are, on the average, two packaging machine breakdowns per week. Assume the weekly machine breakdowns follow a Poisson distribution. Find the mean and standard of this distribution. Find the probability that there are 3 or more machine breakdowns in a given week. Show your work please and thank you in advance.

Answer 1

Given that on the average, two packaging machine breakdowns per week. Let X be the number of weekly machine breakdowns. Thus, X ~ Poisson( = 2)

Mean of the distribution = = 2

Variance of the distribution = = 2

Standard deviation of the distribution = = 1.414214

Probability that there are 3 or more machine breakdowns in a given week = P(X 3)

= 1 - P(X < 3)

= 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

= 1 - [2⁰ * exp(-2)/0! + 2¹ ​* exp(-2)/1! + 2² ​* exp(-2)/2! ]

= 1 - (0.1353 + 0.2707 + 0.2707)

= 0.3233