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

Addition Rule

Statistics

4. Probability

Addition Rule

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1:38 minutes

Problem 3.3.19a

Textbook Question

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)
a. Randomly selecting someone who is under 10 years old

Verified step by step guidance

Step 1: Understand the problem. The goal is to find the probability of randomly selecting someone who is under 10 years old from the U.S. population distribution for 2025. The pie chart provides the percentage distribution of different age groups.

Step 2: Identify the relevant data. From the pie chart, the percentage of the population under 10 years old is given as 12.1%. This percentage represents the proportion of the population in this age group.

Step 3: Convert the percentage to a probability. Probability is expressed as a decimal or fraction. To convert the percentage to a decimal, divide the percentage by 100. For example, \( P(\text{Under 10 years old}) = \frac{12.1}{100} \).

Step 4: Interpret the result. The probability represents the likelihood of randomly selecting someone under 10 years old from the population. Ensure the decimal value is between 0 and 1, as probabilities must fall within this range.

Step 5: Verify the calculation. Double-check the conversion and ensure the probability aligns with the percentage provided in the pie chart.

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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 refers to the chance of randomly selecting an individual from a population who falls into a specific age category, such as those under 10 years old. The probability can be calculated by dividing the number of individuals in the desired age group by the total population.

Pie Chart Interpretation

A pie chart is a circular statistical graphic divided into slices to illustrate numerical proportions. Each slice represents a category's contribution to the whole, with the size of each slice corresponding to the percentage of the population in that category. Understanding how to read and interpret the pie chart is essential for determining the probabilities associated with different age groups in the U.S. population.

Age Distribution

Age distribution refers to the proportion of individuals of different ages within a population. It provides insights into demographic trends and can influence various social and economic factors. In this question, the age distribution data from the pie chart helps identify the percentage of the population that is under 10 years old, which is crucial for calculating the probability of selecting someone from that age group.

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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)a. Randomly selecting someone who is under 10 years old

Key Concepts

Probability

Pie Chart Interpretation

Age Distribution

Watch next

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)
a. Randomly selecting someone who is under 10 years old