Probability problem - finding standard deviation and mean in a normal dist.

[Hamish Cruickshank]

Hey all.

Im doing maths methods 5 (i live in Australia) and I've run into this problem.

A university study investigated the increase in 
heart rates(measured in beats per minute) of 
people undertaking a particular exercise. The 
increases in heart rate were normally distributed 
with a mean of 40 and a standard deviation of 9.

It was determined that the proportion of people 
classified as unfit (x >= 50) is 15% and the 
proportion of people classified as very fit (x <= 22) is 10%. 
Find the mean and standard deviation of the increases 
in heart rate for this university study.

I've no idea how to do this.

Most of these types of problems I have been doing on a graphics calculator, which is allowed and expected in this course. The model of calculator I have is a CASIO fx-9860G AU.

Any help in solving this problem will be greatly appreciated.

Thanks for reading.

 

[Hamish Cruickshank]

Its okay, I got it figured out.

I took the z scores for those percentages as if they were standard normal distributions and then substituted them into the formula z = (x - mu)/sigma. I then had simultaneous equations which were quite easy to solve. I thought i'd answer my own question for anyone who wanted future reference.