Final answer:
The probability that the random variable is between 6.23 and 9.15 is 1.
Step-by-step explanation:
The given random variable has a uniform distribution with parameters (4,6). In a uniform distribution, the probability density function is a constant within a given interval and 0 elsewhere. To find the probability that the random variable is between 6.23 and 9.15, we need to find the area under the probability density function between these points. Since the probability density function is a rectangle, we can find the area by multiplying the base (width) of the rectangle by its height (constant value). The base of the rectangle is (9.15 - 6.23) = 2.92, and the height is 1/2.92 (since the total area under the rectangle must be 1). Therefore, the probability is (2.92 * 1/2.92) = 1.