An absent minded professor will make on average 4 errors in

An absent minded professor will make on average 4 errors in a 12 hour period. Calculate the probability that this professor will make 3 errors or more in 5 hours assuming the poisson process.

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e-? ?x / x!
Where   
? = parameter of the distribution.
x = is the number of independent trials

professor will make on average 4 errors in a 12 hour period
mistake rate of error for 5 hours is 5*4/12 is 1.667

P( X < 3) = P(X=2) + P(X=1) + P(X=0)   
= e^-1.667 * 0 ^ 2 / 2! + e^-1.667 * ^ 1 / 1! + e^-1.667 * ^ 0 / 0!
= 0.7659

P( X > = 3 ) = 1 - P (X < 3) = 0.2341