Ch. 3 - Probability

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 3 - Probability

Problem 3.1.80

Chapter 3, Problem 3.1.80

80. Unusual Events Can any of the events in Exercises 75-78 be considered unusual? Explain.

Verified step by step guidance

Step 1: Understand the concept of 'unusual events' in statistics. An event is considered unusual if its probability is very low, typically less than 0.05 (5%). This threshold helps identify events that are rare or unexpected.

Step 2: Review the events described in Exercises 75-78. Carefully examine the probabilities associated with each event. If the probabilities are not provided, calculate them using the appropriate formulas or data given in the exercises.

Step 3: Compare the calculated probabilities of each event to the threshold of 0.05. If the probability of an event is less than 0.05, it can be classified as unusual.

Step 4: Provide reasoning for why each event is or is not unusual based on the comparison. For example, if an event has a probability of 0.03, it is unusual because it falls below the threshold. Conversely, if an event has a probability of 0.10, it is not unusual.

Step 5: Summarize your findings for all events in Exercises 75-78, clearly stating which events are unusual and providing explanations for each based on their probabilities.

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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. An event with a probability close to 0 is unlikely to happen, while an event with a probability close to 1 is very likely. Understanding probability is essential for determining whether an event is unusual, as it allows us to quantify how often we expect an event to occur in a given context.

Unusual Events

In statistics, an event is often considered unusual if its probability of occurrence is significantly low, typically defined as less than 5%. This threshold helps to identify events that deviate from what is expected based on historical data or theoretical models. Recognizing unusual events is crucial for making informed decisions and understanding the implications of rare occurrences.

Statistical Significance

Statistical significance refers to the likelihood that a relationship or effect observed in data is not due to random chance. It is often assessed using p-values, where a p-value less than 0.05 indicates that the results are statistically significant. This concept is important when evaluating whether the events in Exercises 75-78 can be deemed unusual, as it provides a framework for interpreting the results in a meaningful way.

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Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

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Textbook Question

Matching Probabilities In Exercises 11-16, match the event with its probability.

a. 0.95

b. 0.005

c. 0.25

d. 0

e. 0.375

f. 0.5

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Textbook Question

Warehouse In Exercises 51-54, a warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be

interviewed about the work environment.

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Textbook Question

In Exercises 7-14, perform the indicated calculation.

12. (10C7)/(14C7)

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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.

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