Statistics and uniform distribution

I am having troubles solving the other half of this problem, I got the mean but can't seem to get the numbers correct for probabilities. Steps would be awesome!

A weather forecaster predicts that the May rainfall in a local area will be between 3 and 6 inches but has no idea where within the interval the amount will be. Let x be the amount of May rainfall in the local area, and assume that x is uniformly distributed in the interval 3 to 6 inches.

(a) Calculate the expected May rainfall. μx =4.5
(b) What is the probability that the observed May rainfall will fall within two standard deviations of the mean? Within one standard deviation of the mean? (Round your final answers to 4 decimal places.)
Probability of May rainfall will fall within two SD = ?
Probability of May rainfall will fall within one SD = ?

The question clearly mentions the UNIFORM distribution and so the Normal distribution has nothing to do with it.

For a uniform continuous distribution the standard deviation is
s = (top value - bottom value)/sqrt(12)

So in this case it is (6 - 3)/sqrt(12) = 0.866 (3 dec. pl.)

Can you finish from there?

Edit. For a uniform distribution the probability between any two values is their difference divided by the whole interval.

For one standard deviation each side
(2*0.866)/3 = 0.5773