Weekend Curfews Determine the values of the letters to complete the conditional relative frequency table by column. 16 Years Old 17 Years Old Total 0.9 b 0.88 Before 10 p.m. After 10 p.m. 0.15 0.12 1 Total | 1.0 1.0

To determine the values of the letters in the table, the concept of a relative frequency table needs to be understood. The table categories must sum to 1 (or 100% if expressed as percentages), both in terms of the totals for columns and for rows.

The table provides conditional relative frequencies but is missing a few values (represented by letters). Here's how to find those values:

1. For the "16 Years Old" column, we are given a conditional relative frequency of 0.9 for "Before 10 p.m." Since the total must be 1.0, we can find 'b' (after 10 p.m.) by subtracting 0.9 from 1.0:

b = 1.0 - 0.9 b = 0.10

2. For the "17 Years Old" column, we are missing the value associated with "Before 10 p.m." However, we know that the total should also be 1.0. We have a given value of 0.12 for "After 10 p.m." So we subtract 0.12 from 1.0:

1.0 - 0.12 = 0.88

This is coincidentally the total for "17 Years Old", which indicates that the value for "Before 10 p.m." for "17 Years Old" is 0.88.

3. For the "Total" row, the first value for "Before 10 p.m." is marked with a 'p'. Since the final "Total" value for each column has to be 1.0, we can find 'p' by adding the relative frequencies of the "Before 10 p.m." for both ages and ensure it adds up to the value provided for the "Total" of "Before 10 p.m."(0.88).

So, 0.9 (16 Years Old) + p (17 Years Old) = 0.88 (Total Before 10 p.m.)

However, we've identified that the value for "Before 10 p.m." for "17 Years Old" is 0.88 in the previous step, so we know that 'p' is 0.88.

To summarize: - b = 0.10 for "After 10 p.m." for "16 Years Old" - The value for "Before 10 p.m." for "17 Years Old" is 0.88 (same as the 'p' value) - p = 0.88 for "Before 10 p.m." in the "Total" row

Finished table:

| 16 Years Old | 17 Years Old | Total | |--------------|--------------|--------| | Before 10 p.m. | 0.9 | 0.88 | (p) | After 10 p.m. | 0.10 | 0.12 | (b) | Total | 1.0 | 1.0 |