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?

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?
Transcript text: 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 proability 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?
failed

Solution

failed
failed

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.

Step 1: Total Population

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

Step 2: Probability of Being a Teenager

The ages that qualify as teenagers (ages 1313 to 1919) are 13,14,1713, 14, 17. The number of teenagers is: Number of teenagers=3 \text{Number of teenagers} = 3 Thus, the probability P(teenager)P(\text{teenager}) is calculated as: P(teenager)=Number of teenagersN=38=0.375 P(\text{teenager}) = \frac{\text{Number of teenagers}}{N} = \frac{3}{8} = 0.375

Step 3: Probability of Being at Least 20 Years Old

The ages that are at least 2020 years old are 20,21,22,24,3020, 21, 22, 24, 30. The number of individuals in this age group is: Number at least 20=5 \text{Number at least 20} = 5 Thus, the probability P(at least 20)P(\text{at least 20}) is: P(at least 20)=Number at least 20N=58=0.625 P(\text{at least 20}) = \frac{\text{Number at least 20}}{N} = \frac{5}{8} = 0.625

Step 4: Probability of Being 30 or Older

The only age that is 3030 or older is 3030. The number of individuals in this category is: Number at least 30=1 \text{Number at least 30} = 1 Thus, the probability P(at least 30)P(\text{at least 30}) is: P(at least 30)=Number at least 30N=18=0.125 P(\text{at least 30}) = \frac{\text{Number at least 30}}{N} = \frac{1}{8} = 0.125

Final Answer

The probabilities are as follows:

  • Probability of being a teenager: P(teenager)=0.375P(\text{teenager}) = 0.375
  • Probability of being at least 20 years old: P(at least 20)=0.625P(\text{at least 20}) = 0.625
  • Probability of being 30 or older: P(at least 30)=0.125P(\text{at least 30}) = 0.125

Thus, the final answers are: P(teenager)=0.375,P(at least 20)=0.625,P(at least 30)=0.125 \boxed{P(\text{teenager}) = 0.375, \quad P(\text{at least 20}) = 0.625, \quad P(\text{at least 30}) = 0.125}

Was this solution helpful?
failed
Unhelpful
failed
Helpful