Question

determine whether the statement is true or false. if it is false, rewrite it as a true statement.

the mean of the random variable of a probability distribution describes how the outcomes vary.

choose the correct answer below.

a. the statement is false. the mean of the random variable of a probability distribution describes an uncountable number of possible outcomes. the standard deviation of the random variable of a probability distribution describes how the outcomes vary.
b. the statement is false. the mean of the random variable of a probability distribution describes a countable number of possible outcomes. the variance of the random variable of a probability distribution describes how the outcomes vary.
c. the statement is false. the mean of the random variable of a probability distribution describes a typical outcome. the variance and standard deviation of the random variable of a probability distribution describes how the outcomes vary.
d. true.

Explanation:

Analyze the given statement

The given statement is: "The mean of the random variable of a probability distribution describes how the outcomes vary."

Evaluate the truth value

• The mean (expected value) of a random variable describes the central location or a typical outcome of the probability distribution.
• The variance and standard deviation describe how the outcomes vary (dispersion).
• Therefore, the statement is false.

Identify the correct option

• Option A states the mean describes an uncountable number of possible outcomes, which is incorrect.
• Option B states the mean describes a countable number of possible outcomes, which is incorrect.
• Option C states the statement is false, the mean describes a typical outcome, and the variance and standard deviation describe how the outcomes vary. This is correct.
• Option D states the statement is true, which is incorrect.

Answer:

• (A) The statement is false. The mean of the random variable of a probability distribution describes an uncountable number of possible outcomes. The standard deviation of the random variable of a probability distribution describes how the outcomes vary.
• (B) The statement is false. The mean of the random variable of a probability distribution describes a countable number of possible outcomes. The variance of the random variable of a probability distribution describes how the outcomes vary.
• (C) The statement is false. The mean of the random variable of a probability distribution describes a typical outcome. The variance and standard deviation of the random variable of a probability distribution describe how the outcomes vary. (Correct answer)
• (D) True.