Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 5. Find the probability that exactly six babies will be born during a particular 1-hour period at this hospital.
A) 0.146223
B) 0.000044
C) 0.018278
D) 0.000031

Question

Quizplus · Accepted Answer

The probability of observing exactly k events in a Poisson distribution is given by the formula P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average rate (mean) of occurrence. Here, λ = 5 and k = 6. Plugging these values into the formula gives P(X=6) = (5^6 * e^(-5)) / 6! = 0.146223.

Suppose the Number of Babies Born Each Hour at a Hospital