Final answer:
The probability that a uniformly distributed continuous random variable x is greater than 15, when it is distributed between 10 and 20, is 0.5. This is calculated by the length of the interval from 15 to 20 divided by the total length of the distribution from 10 to 20.
Step-by-step explanation:
A uniform distribution has a constant probability density function (PDF) within a specified interval. In this case, the random variable x is uniformly distributed between 10 and 20, so the PDF is constant within that range.
The total probability for a continuous probability distribution is always 1. Therefore, the probability of x being greater than 15 is equal to the portion of the distribution greater than 15, which is the distance between 15 and 20 divided by the total range of 10 to 20.
Probability = (20 - 15) / (20 - 10) = 0.5
The question pertains to finding the probability that a uniformly distributed continuous random variable x is greater than 15, given that x is uniformly distributed between 10 and 20. First, we note that in a uniform distribution, all intervals of equal length have the same probability. Since the total interval is from 10 to 20, it has a length of 20 - 10 = 10 units.
To find P(x > 15), we look at the interval from 15 to 20, which has a length of 5 units. Hence, the probability that x will be greater than 15 is simply the ratio of the length of the interval from 15 to 20 to the total interval length, which is 5/10 or 0.5.
Therefore, the probability that x is greater than 15 when x is uniformly distributed between 10 and 20 is 0.5, not 0.25 or 1.0 as the options provided suggested.