S2 Normal Distribution help

Hi, I came across this question in the ocr textbook and I'm a bit stuck. Could someone show me how to do it please? It's from Ex 2B p.34

7 (e) Given that X~N(15,4), find s,t,u,v and w correct to 2 d.p.

P(|X-15| < w) = 0.9

The answer is 3.29 but I don't know how to get there!
Thanks very much

Reply 1

RDKGames

Study Forum Helper

Original post by Cometflute

What have you tried?

Reply 2

Cometflute

Original post by RDKGames

What have you tried?

I know that you use z=(x-15)/2 and 15 is the mean so the graph should be like the Z graph except a different height. I tried doing P(|X-15|<w) = 2x P(Z<w) -1 so P(X<w/2) = P(Z<1.282) but that didn't give me the right answer. Maybe you're meant to introduce s= |X-15| for example? But I'm still not sure how to go about solving that...