Which statement about the probability distribution of continuous random variables is false?
A. The probability of all outcomes is represented by the area under the graph line or curve
B. The total area under the graph line or curve is 1.
C. Probability is calculated for a range of values, not just one value.
D. The probability of each value the random variable takes is 1/100

In a continuous probability distribution, the probability of any specific value of the random variable is technically zero, not 1/100 or any other nonzero value. This is because the number of possible values in a continuous distribution is infinite, so assigning a positive probability to any single value would result in the total probability being infinite, which is not permissible.

QueenEndergirl QueenEndergirl · Answer 2 · 2024-05-07T08:26:43-04:00

Answer:

D. The probability of each value the random variable takes is 1/100

Step-by-step explanation:

This statement is false. In the case of continuous random variables, the probability of any specific value is typically zero. This is because continuous random variables can take on an infinite number of values within a given range. Instead of calculating the probability for each individual value, the probability is calculated for a range of values. The probability distribution of continuous random variables is typically represented by a probability density function (PDF), where the probability is represented by the area under the graph line or curve. The total area under the graph line or curve is always equal to 1, ensuring that the probabilities are properly normalized.

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