Final answer:
Without specific information on the probability distribution of times for takeoff clearance at Airport X, the probabilities P(X < 15) and P(X < 5) cannot be calculated. The properties of a transformed random variable Y = 3X - 2 can be determined once the properties of X are known.
Step-by-step explanation:
The question seems to relate to several aspects of probability and statistics, including computing probabilities for specific timeframes and understanding the properties of random variables in relation to airport operations. To calculate the probabilities like P(X < 15) or P(X < 5), one would require information about the probability distribution of the time it takes to obtain clearance for takeoff. Without this data, we cannot compute the probabilities. The random variable Y, defined as Y = 3X - 2, would have its mean and variance affected by this transformation. The mean of Y can be found by applying the transformation to the mean of X, and the variance by applying the transformation rules for variance (since variance is affected by the scaling factor but not by the addition/subtraction of a constant).
For Y = 3X - 2:
- Mean of Y = 3(Mean of X) - 2
- Variance of Y = (3^2)Var(X) (since variance scales with the square of the scaling factor)