A certain town is served by two hospitals. In the larger hospital, about 45 babi

Question

A certain town is served by two hospitals. In the larger hospital, about 45 babies are born each day, and in the smaller hospital, about 15 babies are born each day. Although the overall proportion of boys is about 50 percent, the actual proportion at either hospital may be greater or less than 50 percent on any given day. At the end of a year, which hospital will have the greater number of days on which more than 60 percent of the babies born were boys?
A certain town is served by two hospitals. In the larger hospital, about 45 babies are born each day, and in the smaller hospital, about 15 babies are born each day. Although the overall proportion of boys is about 50 percent, the actual proportion at either hospital may be greater or less than 50 percent on any given day. At the end of a year, which hospital will have the greater number of days on which more than 60 percent of the babies born were boys?
A certain town is served by two hospitals. In the larger hospital, about 45 babies are born each day, and in the smaller hospital, about 15 babies are born each day. Although the overall proportion of boys is about 50 percent, the actual proportion at either hospital may be greater or less than 50 percent on any given day. At the end of a year, which hospital will have the greater number of days on which more than 60 percent of the babies born were boys?

Explanation / Answer

Solution:

The answer is smaller hospital.
The Law of Large Numbers (see the Normative Rules) says:

The more people we survey, the more accurate the result.
Larger samples are better.
In this case, the number of children born each day is a random sample of the number of children born in a year. There is much more deviation in a small (daily, in this case) sample than over an entire year. Similarly, there will be more deviation in a sample of size 15 than in one of size 45. Even though both hospitals will have about 50% boys over the year, the smaller hospital will have more days in which the number is higher than 60% (and more days when it is less than 40%). (Consider the extreme case of a hospital that has one baby a day. Every day will be either more than 60% boys (one) or less than 40% boys (zero).

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.