Textbook Question
"In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.
21. Taking a driver's education course and passing the driver's license exam"
Ch. 3 - Probability
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 3, Problem 3.RE.13
In Exercises 13 and 14, use the table, which shows the approximate distribution of the sizes of firms for a recent year. (Adapted from North American Industry Classification System)
13. Find the probability that a randomly selected firm will have more than four employees.
Verified step by step guidance1
Step 1: Understand the problem. You are tasked with finding the probability that a randomly selected firm will have more than four employees. This means you need to consider all firms with 5 or more employees.
Step 2: Identify the relevant data from the table. The table provides the percentage of firms in different employee size categories: '1 to 4', '5 to 9', '10 to 19', '20 to 99', and '100 or more'.
Step 3: Focus on the categories that represent firms with more than four employees. These categories are '5 to 9', '10 to 19', '20 to 99', and '100 or more'. The corresponding percentages are 11.5%, 4.9%, 4.0%, and 1.1%.
Step 4: Add the percentages for these categories to find the total probability. Use the formula: \( P(>4 \, \text{employees}) = P(5 \text{ to } 9) + P(10 \text{ to } 19) + P(20 \text{ to } 99) + P(100 \text{ or more}) \).
Step 5: Convert the total percentage to a probability by dividing by 100. This will give the probability that a randomly selected firm has more than four employees.
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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 firm with more than four employees from the given distribution. Understanding how to calculate probability is essential for interpreting statistical data and making informed decisions based on that data.
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Cumulative Distribution
A cumulative distribution function (CDF) represents the probability that a random variable takes on a value less than or equal to a certain number. To find the probability of selecting a firm with more than four employees, one must calculate the cumulative percentage of firms with four or fewer employees and subtract it from 100%. This concept is crucial for understanding how probabilities accumulate across different categories.
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Percentages in Statistics
Percentages are a way to express a number as a fraction of 100, making it easier to compare different data sets. In the context of the table, the percentages represent the proportion of firms within specific employee ranges. Understanding how to interpret and manipulate these percentages is vital for answering questions about distributions and probabilities in statistics.
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Related Practice
Textbook Question
In Exercises 1-4, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate.
3. Experiment: Choosing a month of the year
Event: Choosing a month that begins with the letter J
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)
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34. Find the probability of randomly selecting a school with 300 or more students.
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.
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Textbook Question
"In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.
20. Selecting an ace from a standard deck of 52 playing cards, and then selecting a jack from the deck without replacing the ace"
Textbook Question
Telephone Numbers The telephone numbers for a region of Pennsylvania have an area code of 570. The next seven digits represent the local telephone numbers for that region. These cannot begin with a 0 or 1. In Exercises 15 and 16, assume your cousin lives within the given area code.
16. What is the probability of not randomly generating your cousin's telephone number on the first try?