Questions: Question #1 A hypothetical population consists of eight individual ages: 13,14,17,20,21,22,24, and 30 years. a. What is the probability that a person in this population is a teenager? b. What is the probability of selecting a participant who is at least 20 years old? c. What is the probability of selecting a participant that is 30 or older?

Solution Steps

To solve these probability questions, we need to determine the number of favorable outcomes for each scenario and divide it by the total number of individuals in the population.

a. A teenager is typically defined as someone aged 13 to 19. Count the number of individuals in this age range and divide by the total population size.

b. Count the number of individuals who are at least 20 years old and divide by the total population size.

c. Count the number of individuals who are 30 or older and divide by the total population size.

The total number of individuals in the population is given by: \[ N = 8 \]

The ages that qualify as teenagers (ages \(13\) to \(19\)) are \(13, 14, 17\). The number of teenagers is: \[ \text{Number of teenagers} = 3 \] Thus, the probability \(P(\text{teenager})\) is calculated as: \[ P(\text{teenager}) = \frac{\text{Number of teenagers}}{N} = \frac{3}{8} = 0.375 \]

The ages that are at least \(20\) years old are \(20, 21, 22, 24, 30\). The number of individuals in this age group is: \[ \text{Number at least 20} = 5 \] Thus, the probability \(P(\text{at least 20})\) is: \[ P(\text{at least 20}) = \frac{\text{Number at least 20}}{N} = \frac{5}{8} = 0.625 \]

The only age that is \(30\) or older is \(30\). The number of individuals in this category is: \[ \text{Number at least 30} = 1 \] Thus, the probability \(P(\text{at least 30})\) is: \[ P(\text{at least 30}) = \frac{\text{Number at least 30}}{N} = \frac{1}{8} = 0.125 \]

Final Answer