Which of the following probability statements represents a cumulative probability?

• A. $P(X\ne 5)$
• B. $P(X>5)$
• C. $P(X<5)$
• D. $P(X=5)$

Answer: (C)

Verified step by step guidance

1. Understand that a cumulative probability refers to the probability that a random variable \(X\) takes a value less than or equal to a certain number. It is generally expressed as \(P(X \leq x)\) or sometimes \(P(X < x)\) depending on the context.
2. Look at each probability statement and identify whether it represents a cumulative probability or not:
3. - \(P(X \neq 5)\) means the probability that \(X\) is not equal to 5, which is not cumulative.
4. - \(P(X > 5)\) means the probability that \(X\) is greater than 5, which is a tail probability, not cumulative from the left.
5. - \(P(X < 5)\) means the probability that \(X\) is less than 5, which is a cumulative probability from the left side.
6. - \(P(X = 5)\) means the probability that \(X\) equals exactly 5, which is a point probability, not cumulative.
7. Conclude that the statement representing a cumulative probability is the one where \(X\) is less than 5, i.e., \(P(X < 5)\), because it sums probabilities of all outcomes less than 5.