Question

Consider the table below.

Age Group: 18-29, 30-39, 40-49, 50-59, 60-69, 70 and over
Frequency: 9831, 7845, 6869, 6323, 5410, 5279
What is the complement of P(40-59), or P(40-59')?

Answer 1

The complement of the probability of being in the age groups 40-59, denoted as P(40-59'), is calculated by first finding P(40-59), then subtracting it from 1. The result is approximately 0.683, indicating a 68.3% chance of an individual not being in the age groups 40-59.

Step-by-step explanation:

The student has provided a table indicating the frequency of different age groups and requires help in finding the complement of the probability of being in the age groups 40-59, or P(40-59'). To calculate this, we first need to determine the probability of being in the age groups 40-49 or 50-59, which we can find by adding the frequencies of these two groups and then dividing by the total population. After calculating P(40-59), the complement (P(40-59')) is simply 1 - P(40-59).

Step by step, the calculation is as follows:

1. Add the frequencies of the 40-49 and 50-59 age groups: 6869 (40-49) + 6323 (50-59) = 13,192.
2. Now calculate the total population by adding all the frequencies: 9831 (18-29) + 7845 (30-39) + 6869 (40-49) + 6323 (50-59) + 5410 (60-69) + 5279 (70 and over) = 41,557.
3. Calculate P(40-59) by dividing the sum of the frequencies of the age groups 40-49 and 50-59 by the total frequency: P(40-59) = 13,192 / 41,557 ≈ 0.317.
4. Finally, find the complement of P(40-59), which is P(40-59') = 1 - P(40-59) ≈ 1 - 0.317 = 0.683.

Therefore, the complement of P(40-59), or P(40-59'), is approximately 0.683, which means there is a 68.3% chance of an individual being outside the 40-59 age group.