Compute Probabilities of a Poisson Random Variable
-Suppose the number of babies born during an 8-hour shift at a hospital s maternity wing follows a Poisson distribution with a mean of 7 an hour. Find the probability that three babies are born during a particular 1-hour period in this maternity wing.
A) 0.052129
B) 0.046544
C) 0.006516
D) 0.000315

Question

Quizplus · Accepted Answer

The probability of three babies being born during a particular 1-hour period in this maternity wing can be calculated using the Poisson distribution formula:P(X = k) = (e^-λ * λ^k) / k!where:λ is the mean number of babies born per hourk is the number of babies bornIn this case, λ = 7 and k = 3. Plugging these values into the formula, we get:P(X = 3) = (e^-7 * 7^3) / 3! = 0.052129Therefore, the probability that three babies are born during a particular 1-hour period in this maternity wing is 0.052129.