A company that bakes chocolate chip cookies averages 5.2 chocolate chips per cookie. Assume that the number of chocolate chips per cookie follows the Poisson distribution. What is the probability that a randomly selected cookie will contain exactly four chocolate chips?
A)0.3325
B)0.1681
C)0.2960
D)0.2254

Question

Quizplus · Accepted Answer

The probability of a given number of events happening in a fixed interval of time or space if these events happen with a known average rate and independently of the time since the last event is given by the Poisson distribution formula: $P(k; \lambda) = \frac{\lambda^k e^{-\lambda}}{k!}$, where $k$ is the number of occurrences of an event (in this case, 4 chocolate chips), and $\lambda$ is the average number of occurrences (in this case, 5.2 chocolate chips per cookie). Plugging these values into the formula gives: $P(4; 5.2) = \frac{5.2^4 e^{-5.2}}{4!} \approx 0.1681$.

A Company That Bakes Chocolate Chip Cookies Averages 5