nitoha

Here's my take of the question - whenever you see the question saying it is normally distributed, that means you know you need to calculate the z-score. It's just:

z = (X - mu) / sigma = (5 - 10) / 5 = -1.

So you know that 68% falls within your +/- 1 std dev (away from mean). The answer must be larger than 68%. You also know that if 68% falls within +/- 1 std dev, then 1 - 0.68 = 0.32 (or 32%) must fall under the 2 tails.

Since you're only interested in >5, (the right tail), simply half the 32% and add that back to your original 68% and you're done. It's easier to understand, imo, if you just do 68% + 32%, instead of 34% + 50%.

I find it easier to understand, by picturing it on a bell-shaped curve. Hope that helped.