Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

4. Probability

Complements

Statistics

4. Probability

Complements

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2:11 minutes

Problem 3.3.19c

Textbook Question

19. U.S. Age Distribution The projected percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event. (Source: U.S. Census
Bureau)
c. Randomly selecting someone who is not 60 years or over

Verified step by step guidance

Step 1: Identify the age groups that are 60 years or over. From the pie chart, these groups are: 60–69 years (11.9%), 70–79 years (8.6%), and 80 years or older (4.5%).

Step 2: Add the percentages of these age groups to find the total percentage of the population that is 60 years or over. Use the formula: Total percentage = 11.9% + 8.6% + 4.5%.

Step 3: Subtract the total percentage of the population that is 60 years or over from 100% to find the percentage of the population that is not 60 years or over. Use the formula: Percentage not 60 years or over = 100% - Total percentage of 60 years or over.

Step 4: Convert the percentage of the population that is not 60 years or over into a probability. Since probability is expressed as a decimal, divide the percentage by 100. Use the formula: Probability = Percentage / 100.

Step 5: Interpret the result. The probability represents the likelihood of randomly selecting someone who is not 60 years or over from the U.S. population in 2025.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the chance of randomly selecting an individual from a specific age group based on the distribution percentages shown in the pie chart.

Complementary Events

Complementary events are pairs of outcomes in probability that cover all possible outcomes of an experiment. For instance, in this question, selecting someone who is not 60 years or older is the complement of selecting someone who is 60 years or older, allowing for easier probability calculations.

Pie Chart Interpretation

A pie chart visually represents data in a circular format, where each slice corresponds to a category's proportion of the whole. Understanding how to read the pie chart is crucial for determining the age distribution percentages, which are necessary for calculating the required probabilities.

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19. U.S. Age Distribution The projected percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event. (Source: U.S. CensusBureau)c. Randomly selecting someone who is not 60 years or over

Key Concepts

Probability

Complementary Events

Pie Chart Interpretation

Watch next

19. U.S. Age Distribution The projected percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event. (Source: U.S. Census
Bureau)
c. Randomly selecting someone who is not 60 years or over