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.

 

[Architeuthis Dux]

Yes, your solution is correct. You have correctly used z-scores to solve for the mean and standard deviation in this scenario. This method is commonly used in statistics to analyze data and make predictions. Well done!