Problem 1

The distribution of ages in the United States in the year 2010 is given below. Intervals include the left endpoint but not the right; the number of people aged 100 or more was not zero but it was so small that it makes no difference to the table. You can assume that the ages are uniformly distributed within each interval.
Age (Years) Percent
0-5 6.6
5-15 13.3
15-20 7.1
20-30 13.8
30-45 19.8
45-60 20.9
60-75 12.5
75-100 6.0
Source: Adapted from Statistical Abstract 2012
: 3.0 points

Each part is worth 1 point.

a) Which interval contained more people: 5-15 or 15-20?
5-1515-20

b) Which interval was more crowded: 5-15 or 15-20?
5-1515-20

c) Were there more 5-year-olds or 15-year-olds?
5-year-olds15-year-olds

a) 5-15

b) 15-20

c) 15-year-olds

To answer these questions, we need to compare the percentages given in the table.

a) To determine which interval contained more people, we compare the percentage values for the intervals 5-15 and 15-20. Looking at the table, we see that the percentage for the 5-15 interval is 13.3%, while the percentage for the 15-20 interval is 7.1%. Therefore, the 5-15 interval contained more people.

b) To determine which interval was more crowded, we compare the percentages again. The percentage for the 5-15 interval is 13.3%, while the percentage for the 15-20 interval is 7.1%. Since the percentage for the 5-15 interval is larger, that interval was more crowded.

c) To determine if there were more 5-year-olds or 15-year-olds, we need to look at the specific age ranges within the intervals. The 5-15 interval represents ages from 5 to 14, while the 15-20 interval represents ages from 15 to 19. Since the 5-15 interval covers a larger age range, it includes both 5-year-olds and 15-year-olds. Therefore, there were more 5-year-olds than 15-year-olds in this case.