Confidence Intervals


I am new to stats and really spending lots of time on concepts which I can build on, I thought I was fairly comfortable with confidence intervals until I came across the question below and have been struggling to get my head around this.

Let X be a uniformly distributed random variable between 1 and -1, and the standard deviation of x is .577, then what % of distributions will be less than 1.96 standard deviations above the mean ?



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This doesn't really have anything to do with confidence intervals - it's just a simple probability calculation. Do you know how to calculate probability with respect to a uniform distribution?
I am new to stats, came across the question above and did not really understand it. Have been reading up on probability distributions and building up my concepts. For the above question I am looking for an explanatory answer and not necessarily the mathematical solution. Hope you can help.Thanks