Questions: Multiple Choice Question The area under a uniform distribution (or any probability distribution) represents a probability. Which one of the following statements characterizes this area? - The area will be greater than one, because each probability has one as an upper limit. - The area will be less than one, because a probability is always less than one. - Area to the left of the mean is negative and area to the right of the mean is positive. - The total area is one.

Solution Steps

The problem is a multiple-choice question about the area under a uniform distribution (or any probability distribution) and its properties.

The statements provided are:

1. The area will be greater than one, because each probability has one as an upper limit.
2. The area will be less than one, because a probability is always less than one.
3. Area to the left of the mean is negative and area to the right of the mean is positive.
4. The total area is one.

1. The area under a probability distribution represents the total probability, which is always 1 for a complete distribution.
2. The area under the curve of a probability distribution is exactly 1, not less than 1.
3. Probabilities are always non-negative; areas under the curve are not negative.
4. The total area under the curve of a probability distribution is indeed 1.

Final Answer