Question

practice working with relative frequency tables.
weekend curfews
determine the values of the letters to complete the conditional relative frequency table by column.
16 years old\t17 years old\ttotal
a =
b =
before 10 p.m.\t0.9\tb\t0.88
b =
after 10 p.m.\ta\t0.15\t0.12
total\t1.0\t1.0\t1.0

Explanation:

Step1: Find \( a \)

For the "16 Years Old" column, the total is \( 1.0 \). The sum of "Before 10 p.m." and "After 10 p.m." should be \( 1.0 \). So, \( 0.9 + a = 1.0 \). Solving for \( a \), we get \( a = 1.0 - 0.9 = 0.1 \).

Step2: Find \( b \)

For the "17 Years Old" column, the total is \( 1.0 \). The sum of "Before 10 p.m." and "After 10 p.m." should be \( 1.0 \). So, \( b + 0.15 = 1.0 \). Solving for \( b \), we get \( b = 1.0 - 0.15 = 0.85 \).

Answer:

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