There are two hospitals; one averages 45 births per day,the other 15 births per day.You are asked,"In any given year,which hospital will have a higher percentage of days during which more than 60 percent of the babies born will be male?" The correct answer is __________.
A)the "45" hospital
B)the "15" hospital
C)that there is an equal chance of either
D)that there is insufficient information provided (thus,we cannot answer the question)

Question

Quizplus · Accepted Answer

We can use the binomial distribution to calculate the probability of having more than 60% male babies on any given day at each hospital. Let p1 = probability of male birth at the "45" hospital and p2 = probability of male birth at the "15" hospital. Assuming an equal chance of having a male or female baby, p1 = p2 = 0.5.

For the "45" hospital, the probability of having more than 60% male babies on any given day is:
P(X > 0.6*45) = P(X > 27) = 1 - binomdist(27, 45, 0.5, true) ≈ 0.015

For the "15" hospital, the probability of having more than 60% male babies on any given day is:
P(X > 0.6*15) = P(X > 9) = 1 - binomdist(9, 15, 0.5, true) ≈ 0.226

Therefore, the "15" hospital is more likely to have a higher percentage of days during which more than 60% of the babies born will be male.

There Are Two Hospitals; One Averages 45 Births Per Day,the