In a probability histogram, there is a correspondence between —.

• A. the number of bars and the total probability
• B. the area of each bar and the probability of the corresponding class interval
• C. the width of each bar and the standard deviation σ
• D. the height of each bar and the mean of the data μ

Answer: (B)

Verified step by step guidance

1. Understand that a probability histogram is a graphical representation of a probability distribution for a continuous random variable.
2. Recall that in a probability histogram, the total area under all the bars equals 1, representing the total probability of all outcomes.
3. Recognize that each bar corresponds to a class interval (or bin) of the data, and the area of that bar represents the probability that the variable falls within that interval.
4. Note that the height of each bar is the probability density, which when multiplied by the width of the class interval gives the area (probability) of that bar.
5. Therefore, the key correspondence in a probability histogram is between the area of each bar and the probability of the corresponding class interval.