Question

weekend curfews
determine the values of the letters to complete the conditional relative frequency table by column.
16 years old 17 years old total
before 10 p.m. 0.9 b 0.88
a =
after 10 p.m. a 0.15 0.12
b =
total 1.0 1.0 1.0

Explanation:

Step1: Use column - total relationship for 16 - year - olds

In the column for 16 - year - olds, the sum of the relative frequencies of "Before 10 p.m." and "After 10 p.m." must be 1. Since the relative frequency of "Before 10 p.m." for 16 - year - olds is 0.9, we can find \(a\) as follows.
Let \(a\) be the relative frequency of "After 10 p.m." for 16 - year - olds. Then \(0.9 + a=1\).
Solving for \(a\): \(a = 1 - 0.9=0.1\)

Step2: Use column - total relationship for 17 - year - olds

In the column for 17 - year - olds, the sum of the relative frequencies of "Before 10 p.m." and "After 10 p.m." must be 1. Since the relative frequency of "After 10 p.m." for 17 - year - olds is 0.15, we can find \(b\) as follows.
Let \(b\) be the relative frequency of "Before 10 p.m." for 17 - year - olds. Then \(b+0.15 = 1\).
Solving for \(b\): \(b=1 - 0.15 = 0.85\)

Answer:

\(a = 0.1\)
\(b = 0.85\)