We are given the following probabilities for the continuous random variable $X$:

• $P(25 \leq X \leq 73) = 0.28$
• $P(X > 73) = 0.12$

Step-by-step solution:

1. Calculate $P(X < 73)$: The total probability for any continuous random variable is 1. Therefore: $P(X < 73) = 1 - P(X > 73)$ Substituting the given probability: $P(X < 73) = 1 - 0.12 = 0.88$

2. Calculate $P(X < 25)$: We can break down the probabilities around 25 and 73 as follows: $P(25 \leq X \leq 73) + P(X < 25) + P(X > 73) = 1$ Rearranging this: $P(X < 25) = 1 - P(25 \leq X \leq 73) - P(X > 73)$ Substituting the known values: $P(X < 25) = 1 - 0.28 - 0.12 = 0.60$

3. Calculate $P(X = 73)$: Since $X$ is a continuous random variable, the probability of it taking any exact value is 0. Therefore: $P(X = 73) = 0$

Final answers:

• $P(X < 73) = 0.88$
• $P(X < 25) = 0.60$
• $P(X = 73) = 0$

Would you like further details or have any questions?

Related Questions:

1. How would you calculate $P(X > 25)$?
2. What is the cumulative distribution function (CDF) based on this data?
3. How do you find the probability if the distribution was discrete instead of continuous?
4. What if $P(X > 25)$ was given, how would that change the calculations?
5. How can you use this information to calculate the mean or variance of $X$?

Tip: For continuous random variables, the probability of an exact value is always zero. This is a key property that distinguishes continuous distributions from discrete ones.