Answer to Question #153377 in Statistics and Probability for John

Question

Assume that in a crowded class, on average 3 students attempt to cheat in any given exam. For a course which will have 2 midterms and 1 final exam in each semester, what is the probability that there will be less than 5 cheating attempts in this course’s exams for any given semester?

Answer 1

On average there are 3*3=9 cheating attempts for a semester.

A - there will be less than 5 cheating attempts in this course’s exams for any given semester.

Let's use Poisson Distribution to find P(A):

P(A) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=

$e^{-9}*9^0/0!+e^{-9}*9^1/1!+e^{-9}*9^2/2!+e^{-9}*9^3/3!+e^{-9}*9^4/4!=$

0.00012+0.00111+0.00500+0.01499+0.03374 = 0.055