Solving Normal Curve Questions using z-scores

[Aftermarth]

ok. mean (\mu\) and standard deviation (\sigma\) are unknown.
20% of people scored less than 45
and the top 15% scored greater than 87

thus:
P(x \leq\ 45) = .2
P(x > 87) = 0.15, which needs to be converted to P(x \leq\ 87 ) = 0.85

now using z scores ( z - \mu\) / \sigma\
for part one:
(45 - \mu\) / \sigma\ = inverse normal (0.2)
= -0.8416...
rearranging to make 45 the subject:
-0.8416\sigma\ + \mu\ = 45

and for part 2:
(87 - \mu\) / \sigma\ = inverse normal (0.85)
= 1.03643...
rearranging to make 87 the subject:
1.03643\sigma\ + \mu\ = 87

this leaves to simulataneous equations:
-0.8416\sigma\ + \mu\ = 45
1.03643\sigma\ + \mu\ = 87

which can be solved to give:
\mu\ = 63.8
\sigma\ = 22.4

am i correct?

 

[EnumaElish]

Yes.