The maternity ward at Dr. Jose Fabella Memorial Hospital in Manila in the Philippines is one of the busiest in the world with an average of 60 births per day. Let X = the number of births in an hour.

Question

What is the mean?

What is the standard deviation?

What is the probability that the maternity ward will deliver three babies in one hour? 

What is the probability that the maternity ward will deliver at most three babies in one hour?

What is the probability that the maternity ward will deliver more than five babies in one hour?

Answer 1

Assuming births are independent of each other (they should be), you could use the Poisson distribution where λ = 60/24.

Now, μ=λ and σ=√λ. Perhaps you need to prove these. That would be a great exercise, and perhaps you would need a tutor to help guide you through.

To calculate probabilities, your calculator may have the Poisson distribution. Otherwise you would use this:

P(X=k) = λ^k e^-λ/ k!

What is the probability that the maternity ward will deliver at most three babies in one hour?

p = P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

What is the probability that the maternity ward will deliver more than five babies in one hour?

p = 1 - P(X<6)

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