Hey Danthemaths.

P(Y > 45) = 0.12 implies

P(Y - 40 > 45 - 40) = 0.12 implies

P([Y - 40]/sigma > (45-40)/sigma) = 0.12 implies

P(Z > 5/sigma) = 0.12 implies

P(Z > z) = 0.12 where 5/sigma = z which finally implies

P(Z < z) = 1 - P(Z > z) = 1 - 0.12 = 0.88

Now use Normal tables to get the value of z and use the fact that z = 5/sigma or in other words, sigma = 5/z.

This is a tricky question.