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?

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.