Ch. 5 - Discrete Probability Distributions

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 5 - Discrete Probability Distributions

Problem 5.RE.6

Chapter 5, Problem 5.RE.6

Acrophobia USA Today reported results from a survey in which subjects were asked if they are afraid of heights in tall buildings. The results are summarized in the accompanying table. Does this table describe a probability distribution? Why or why not?

Verified step by step guidance

Step 1: Understand the concept of a probability distribution. A probability distribution must satisfy two conditions: (1) The sum of all probabilities must equal 1, and (2) each probability value must be between 0 and 1 inclusive.

Step 2: Examine the table provided. The table lists two responses ('Yes' and 'No') along with their corresponding probabilities P(x): 0.46 for 'Yes' and 0.54 for 'No'.

Step 3: Verify the first condition of a probability distribution. Add the probabilities: P(Yes) + P(No) = 0.46 + 0.54. Check if the sum equals 1.

Step 4: Verify the second condition of a probability distribution. Ensure that each probability value (0.46 and 0.54) lies within the range [0, 1].

Step 5: Based on the results of the verification steps, determine whether the table satisfies both conditions of a probability distribution and explain why or why not.

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Key Concepts

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

Probability Distribution

A probability distribution describes how the probabilities of a random variable are distributed across its possible values. For a valid probability distribution, the sum of all probabilities must equal 1, and each individual probability must be between 0 and 1. In the context of the survey, the responses 'Yes' and 'No' with their respective probabilities must satisfy these conditions.

Random Variable

A random variable is a numerical outcome of a random phenomenon. In this case, the random variable could be defined as the response to the question of whether individuals are afraid of heights. The responses 'Yes' and 'No' represent the possible outcomes of this random variable, which can be analyzed using probability distributions.

Sum of Probabilities

The sum of probabilities in a probability distribution must equal 1, reflecting the certainty that one of the possible outcomes will occur. In the provided table, the probabilities for 'Yes' (0.46) and 'No' (0.54) add up to 1 (0.46 + 0.54 = 1.00), confirming that the table represents a valid probability distribution.

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Textbook Question

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Textbook Question

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Textbook Question

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