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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1:57 minutes

Problem 3.RE.34

Textbook Question

In Exercises 33 and 34, use the pie chart at the left, which shows the percent distribution of the number of students in U.S. public schools in a recent year. (Source: U.S. National Center for Education Statistics)

34. Find the probability of randomly selecting a school with 300 or more students.

Verified step by step guidance

Identify the relevant categories in the pie chart that represent schools with 300 or more students. These categories are '300–499', '500–999', and '1000 or more'.

Determine the percentage of students in each of these categories from the pie chart: '300–499' is 28.1%, '500–999' is 32.7%, and '1000 or more' is 9.4%.

Add these percentages together to find the total percentage of students in schools with 300 or more students. Use the formula: Total Percentage = Percentage(300–499) + Percentage(500–999) + Percentage(1000 or more).

Convert the total percentage into a probability. Since percentages are out of 100, divide the total percentage by 100 to express it as a probability.

Interpret the result as the probability of randomly selecting a school with 300 or more students.

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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 a school with 300 or more students from the total distribution shown in the pie chart.

Pie Chart Interpretation

A pie chart visually represents data as slices of a circle, where each slice corresponds to a category's proportion of the whole. Understanding how to read the percentages in the pie chart is essential for determining the probability of selecting a school based on its student population.

Cumulative Distribution

Cumulative distribution refers to the total percentage of observations that fall below a certain value. To find the probability of selecting a school with 300 or more students, one must calculate the cumulative percentage of schools with fewer than 300 students and subtract it from 100%.

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Textbook Question

29. Explain, in your own words, why in the Addition Rule for P(A or B or C), P(A and B and C) is added at the end of the formula.

Textbook Question

In Exercises 25 and 26, determine whether the events are mutually exclusive. Explain your reasoning.

25. Event A: Randomly select a red jelly bean from a jar.

Event B: Randomly select a yellow jelly bean from the jar.

Textbook Question

28. A sample of 6500 automobiles found that 1560 of the automobiles were black, 3120 of the automobiles were sedans, and 1170 of the automobiles were black sedans. Find the probability that a randomly chosen automobile from this sample is black or a sedan.

Textbook Question

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31. A 12-sided die, numbered 1 to 12, is rolled. Find the probability that the roll results in an odd number or a number less than 4.

Textbook Question

39. You are given that P(A) = 0.15 and P(B) = 0.40. Do you have enough information to find P(A or B)? Explain.

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)

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Textbook Question

Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)

b. Randomly selecting a person from the sample who is conservative or very conservative

Textbook Question

Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)

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In Exercises 33 and 34, use the pie chart at the left, which shows the percent distribution of the number of students in U.S. public schools in a recent year. (Source: U.S. National Center for Education Statistics)34. Find the probability of randomly selecting a school with 300 or more students.

Key Concepts

Probability

Pie Chart Interpretation

Cumulative Distribution

Watch next

In Exercises 33 and 34, use the pie chart at the left, which shows the percent distribution of the number of students in U.S. public schools in a recent year. (Source: U.S. National Center for Education Statistics)

34. Find the probability of randomly selecting a school with 300 or more students.