THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
On average,there are 3.2 defects in a sheet of rolled steel.Assume that the number of defects follows a Poisson distribution.
-What is the probability of having more than three defects in a roll?
A)0.354
B)0.398
C)0.412
D)0.621

Question

Quizplus · Accepted Answer

To solve, we need to use the Poisson probability formula:
P(X > 3) = 1 - P(X ≤ 3)
= 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)]
= 1 - [(e^-3.2 * 3.2^0 / 0!) + (e^-3.2 * 3.2^1 / 1!) + (e^-3.2 * 3.2^2 / 2!) + (e^-3.2 * 3.2^3 / 3!)]
= 1 - [(0.0404 + 0.1293 + 0.2069 + 0.2223)]
= 1 - 0.599
= 0.401 or 0.398 (rounded to three decimal places)
Therefore, the best choice is B.