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Chapter 8: Problem 24

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The area of a histogram associated with a probability distribution is a number between 0 and 1 .

Short Answer

Expert verified
The statement is true. The area of a histogram associated with a probability distribution is a number between 0 and 1 because each bar in the histogram represents the probability of a specific outcome, and the probability of each outcome must be between 0 and 1 according to the properties of a probability distribution.

Step by step solution

01

Recall the properties of a probability distribution

A probability distribution must satisfy two properties: 1. The probability of each outcome is between 0 and 1, inclusive: \(0 \le P(x) \le 1\). 2. The sum of probabilities of all outcomes is equal to 1: \(\sum P(x) = 1\).
02

Analyzing the area of a histogram

In a histogram, the area of any particular bar corresponds to the probability of that particular outcome. Since a histogram represents the probability distribution, it must also follow the properties of a probability distribution, as mentioned above.
03

Answer the question

The area of a histogram associated with a probability distribution is a number between 0 and 1 because each bar in the histogram represents the probability of a specific outcome, and the probability of each outcome must be between 0 and 1 according to the properties of a probability distribution. The statement in the exercise is true.

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Most popular questions from this chapter

A probability distribution has a mean of 20 and a standard deviation of 3 . Use Chebychev's inequality to find a bound on the probability that an outcome of the experiment lies between a. 15 and 25 . b. 10 and 30 .

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