A brick manufacturer produces 25 bricks per hour Historicall

A brick manufacturer produces 25 bricks per hour. Historically, the process has produced a constant 1% non-conforming bricks.   Let X = the number of non-conforming bricks produced in a given hour (so that X follows the Binomial Distribution).

a.               What is the probability that at least one non-conforming brick is produced in the next hour (at least one of the next 25)?

Solution

Given X follows Binomial distribution with n=25 and p=0.01

P(X=x)=25Cx*(0.01^x)*(0.99^(25-x)) for x=0,1,2,...,25

So the probability is

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

=1-25C0*(0.01^0)*(0.99^(25-0))

=0.2221786