How to find the unknown deviation from this problem!

I am a bit stuck on how to find the standard deviation of this question. I know the formula u need to use: x-(x bar) / Z .. But I dont know how to find the Z score!

Could you please help me with (1) find the Z score value and (2) getting to the answer...

The question being:
Monica walks to work from home and she uses route a or route b.
Her journey time, Y minutes by route B may be assumed to be normally distributed with a mean of 40 and an unknown standard deviation.
Given that P(Y > 45) = 0.12, calculate the standard deviation value.

I would really appreciate some helpful feedback and solutions!

Thanks in advance
Dan

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.