Determine whether any of the events in Exercise 33 are unusual. E...

6. Normal Distribution and Continuous Random Variables

Standard Normal Distribution

Statistics

6. Normal Distribution and Continuous Random Variables

Standard Normal Distribution

2:21 minutes

Problem 5.R.35

Textbook Question

Determine whether any of the events in Exercise 33 are unusual. Explain your reasoning.

Verified step by step guidance

Identify the events mentioned in Exercise 33 and determine their probabilities. An event is considered unusual if its probability is very low, typically less than 0.05 (5%).

Calculate the probability of each event using the given data or formulas. For example, if the problem involves binomial probabilities, use the binomial probability formula:

P (X = k) = \frac{n!}{k! (n - k)!} \cdot p^{k} \cdot (^{1 - p) n - k}

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 is considered unusual.

Explain why an event is unusual based on its low probability. For example, you might say, 'This event is unusual because its probability is less than 0.05, indicating it is unlikely to occur under normal circumstances.'

Summarize your findings by listing which events are unusual and which are not, along with their respective probabilities and reasoning.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unusual Events

In statistics, an event is 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 under normal circumstances, prompting further investigation or consideration.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. Understanding probability is essential for determining whether an event is unusual, as it quantifies how often we expect an event to happen based on historical data or theoretical models.

Statistical Significance

Statistical significance refers to the likelihood that a result or relationship observed in data is not due to random chance. In the context of unusual events, determining statistical significance helps to assess whether the occurrence of an event is noteworthy and warrants further analysis or action.

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