Examine Figure 6-37. Government documents and the Census Bureau show that the age at first marriage for

Question:

Examine Figure 6-37. Government documents and the Census Bureau show that the age at first marriage for U.S. citizens is approximately normally distributed for both men and women. For men, the average age is about 27 years, and for women, the average is about 24 years. For both sexes, the standard deviation is about 2.5 years.
(a) If the distribution is symmetrical and mound-shaped (such as the normal distribution), why would you expect the median, mean, and mode to be equal?
(b) Consider the age at first marriage in 1995. What is the probability that a man selected at random was over age 30 at the time of his first marriage? What is the probability that he was under age 20? What is the probability that he was between 20 and 30?
(c) Consider the age at first marriage in 1995. What is the probability that a woman selected at random was over age 28 at the time of her first marriage? What is the probability that she was under age 18? What is the probability that she was between 18 and 28?
(d) At what age were only 10% of eligible men (who had never been married before) unmarried? At what age were only 5% unmarried?
(e) At what age were only 10% of eligible women (who had never been married before) unmarried? At what age were only 5% unmarried?
(f) The Census Bureau tracks data about marriages and age at first marriage. The Statistical Abstract of the United States is published each year and contains tables giving this information. For more information, visit the Brase/Brase statistics site at college.hmco.com/pic/braseUS9e and find the link to the Census Bureau. Look for marriage under the subject index, and follow the links to the table. Using either the Abstract or the Census Bureau web site, find the most recent information about median age at first marriage. Although the median age changes from year to year, the standard deviation usually does not change much. Under the assumption that the age at first marriage follows a distribution that is approximately normal, the mean age at first marriage equals the median age. Using a standard deviation of about 2.5 years, repeat parts (b) through (e) for the most recent year for which median age at first marriage is available.