Ch. 4 - Discrete Probability Distributions

Larson - Elementary Statistics: Picturing the World 8th Edition

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Larson 8th Edition

Ch. 4 - Discrete Probability Distributions

Problem 4.1.23

Chapter 4, Problem 4.1.23

Unusual Events In Exercise 19, would it be unusual for a household to have no HD televisions? Explain your reasoning.

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Identify the statistical context of the problem: Determine whether the event of a household having no HD televisions is considered unusual. This typically involves analyzing probabilities or proportions.

Define the threshold for an unusual event: In statistics, an event is often considered unusual if its probability is less than 0.05 (5%).

Gather the necessary data: Look for the probability or proportion of households that have no HD televisions. This information might be provided in the exercise or can be derived from a given distribution.

Compare the probability to the threshold: If the probability of a household having no HD televisions is less than 0.05, then it is considered unusual. Otherwise, it is not unusual.

Explain the reasoning: Clearly state whether the event is unusual based on the comparison and provide a justification using the probability and the threshold value.

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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 the context of households having HD televisions, understanding the probability of a household owning one can help determine if having none is unusual. If the probability of ownership is high, then having no HD televisions would be considered an unusual event.

Statistical Significance

Statistical significance refers to the likelihood that a relationship observed in data is not due to random chance. In this scenario, determining whether it is unusual for a household to have no HD televisions involves assessing how many households typically own them. If the proportion of households without HD televisions is significantly lower than expected, it would be deemed unusual.

Normal Distribution

Normal distribution is a probability distribution that is symmetric about the mean, indicating that data near the mean are more frequent in occurrence than data far from the mean. In analyzing household ownership of HD televisions, understanding the normal distribution can help identify what constitutes typical versus unusual ownership patterns, allowing for a clearer assessment of whether having no HD televisions is an outlier.

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Textbook Question

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Textbook Question

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