The question goes...

*An athlete finds that in the long jump his distances form a Normal distribution with mean 8.2 metres and standard deviation 0.24 metres. In a competition he is currently in second place with one more jump left to take. The current leader has jumped a distance of 8.5 metres. Find the probability that, on his next jump, he:* **(a) **takes the gold medal; (I've done this and got an answer of 0.1056)

**(b) **takes the gold medal, but doesn't quite manage to break the long jump world record of 8.9 metres. **(c)** What distance can this athlete expect to exceed once in 500 jumps?
It's part (b) that I'm stuck on really. I know it's a

kind of thing, and I know (or I think I do!) that is just...

...but then I'm not sure how to go about calculating the numerator (since I already know the denominator from part (a)) of that from there.

I did think for a while that the numerator was the same as

, but that got a silly answer i.e. an answer bigger than 1.