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

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

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2:12 minutes

Problem 3.1.80

Textbook Question

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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Textbook Question

Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.

34. A spreadsheet is used to randomly generate a number from 1 to 4000. Event B is generating a number less than 500.

Textbook Question

Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.

43. Event C: rolling a number greater than 4

Textbook Question

Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.

46. Event F: rolling a number divisible by 5

Textbook Question

Boy or Girl? In Exercises 71-74, a couple plans to have three children. Each child is equally likely to be a boy or a girl.

71. What is the probability that all three children are girls?

Textbook Question

81. Genetics A Punnett square is a diagram that shows all possible gene combinations in a cross of parents whose genes are known. When two pink snapdragon flowers (RW) are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring: red (RR), pink (RW), pink (WR), and white (WW), as shown in the Punnett square at the left. When two pink snapdragons are crossed, what is the probability that the offspring will be (c) white?

Textbook Question

87. College Football A stem-and-leaf plot for the numbers of touchdowns allowed by the 127 NCAA Division I Football Bowl Subdivision teams in the 2020-2021 season is shown. Find the probability that a team chosen at random allowed (a) at least 51 touchdowns. Are any of these events unusual? Explain. (Source: National Collegiate Athletic Association)

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Textbook Question

97. Rolling a Pair of Dice You roll a pair of six-sided dice and record the sum.

a. List all of the possible sums and determine the probability of rolling each sum.

b. Use technology to simulate rolling a pair of dice and record the sum 100 times. Make a tally of the 100 sums and use these results to list the probability of rolling

each sum.

c. Compare the probabilities in part (a) with the probabilities in part (b). Explain any similarities or differences.

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

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