Hints:
The mean for a uniform distribution is the average of the left and the right endpoints.
The standard deviation for a uniform distribution is the square root of (b - a)2 / 12 where a and b are the left and right endpoints respectively.
For a uniform distribution, the probability that an outcome will be exactly a given number is always 0.
For a uniform distribution, the probability that an outcome will be between two numbers x and y is (y - x) / (b - a) where a and b are the left and right endpoints respectively.
In general for a uniform distribution, we can find a probability by taking the length of the described line segment and divide by b - a.
To find a percentile, p
(or a quartile: 25th or
75th percentile) you want to go
backwards with the uniform distribution calculations. Here you know
the probability and want to find y, so you set
p = (y -
a) / (b - a) and solve for
y.
If you have a uniform distribution and want to find a conditional probability P(A|B), then use the given to get the new endpoints. For example if the distribution is uniform between 5 and 20 and you want to find the probability of an event being between 10 and 17 given that the outcome is less than or equal to 15, you need to find the probability that an event is between 10 and 15 for a uniform distribution with endpoints 5 and 15.