Final answer:
The question lacks specific values for which to solve but generally in a uniform distribution U(1, 5), the mean is the midpoint of the range and standard deviation can be calculated using the respective formulas.
Step-by-step explanation:
Understanding the Uniform Distribution
In the uniform distribution U(a, b), all values within the range from a to b are equally likely to occur. This question appears to lack specific probability statements that need to be true for a given value of a. However, for any uniform distribution U(a, b), the mean µ is given by the formula µ = (a + b) / 2, and since the range is from 1 to 5, the mean would be (1 + 5) / 2 = 3. The mean is the midpoint of the distribution since all values are equally likely. The standard deviation σ is calculated using the formula σ = √((b - a)^2 / 12). For this distribution, σ = √((5 - 1)^2 / 12) = √(16 / 12) = √(4 / 3).
If a random variable X follows this distribution, the probability P(x > a) can be determined as the area under the probability density function (pdf) from point a to point b. This can also be found by simply calculating the length of the interval (b - a) and dividing by the entire range of the distribution, which yields P(x > a) = (b - a) / (b - a), whenever a is within the range [1,5].