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For a continuous random variable X, P(29 ≤ X ≤ 79) = 0.17 and P(X > 79) = 0.25. Calculate the following probabilities. (Round your answers to 2 decimal places.) a. P(X < 79) b. P(X < 29) c. P(X = 79)

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Answer:

I can help you with the probabilities for a continuous random variable. Here are the steps and the results:

To calculate the probabilities, we need to use the properties of probability and the given information. For a continuous random variable X, the following properties hold:

The total probability is 1, i.e., P(X < ∞) = 1

The probability of a complement event is 1 minus the probability of the original event, i.e., P(X < a) = 1 - P(X ≥ a)

The probability of an interval is the difference of the probabilities of the endpoints, i.e., P(a ≤ X ≤ b) = P(X ≤ b) - P(X ≤ a)

Using these properties and the given information, we can calculate the following probabilities:

P(X < 79) = 1 - P(X ≥ 79) = 1 - (P(29 ≤ X ≤ 79) + P(X > 79)) = 1 - (0.17 + 0.25) = 0.58

P(X < 29) = 1 - P(X ≥ 29) = 1 - (P(29 ≤ X ≤ 79) + P(X > 79)) = 1 - (0.17 + 0.25) = 0.58

P(X = 79) = 0, because for a continuous random variable, any single outcome has zero probability.

Therefore, the answers are:

a. P(X < 79) = 0.58

b. P(X < 29) = 0.58

c. P(X = 79) = 0

I hope this helps you understand how to calculate probabilities for a continuous random variable. If you have any questions, please let me know.

User Alexander R
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