In a study of how people make probability judgments, college students (with no background in probability or statistics) were asked the following question.10 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. As you know, about 50% of all babies are boys. The exact percentage of baby boys, however, varies from day to day. Sometimes it may be higher than 50%, sometimes lower.
For a period of 1 year, each hospital recorded the days on which at least 60% of the babies born were boys. Which hospital do you think recorded more such days?
• The larger hospital
• The smaller hospital
• About the same (i.e., within 5% of each other)
Determine the correct answer by using the normal approximation (without the continuity correction) to calculate the appropriate probabilities.