normal distribution and z scores

[maxpower2]

im trying to find the mean and standard deviation for player A finishing positions in a tournament.

we know 15% he finishes in the top 10.
we know 10% he finishes in the bottom 20

https://www.youtube.com/watch?v=t727GFJB-ZU

i was watching above for how to do this on paper. there is a slight difference in what im using this method for. so if any maths guys could let me know if this is the wrong method for the problem.

i can make the formulas p(z<a)=15%
and p(z<b)=90%

i use the =norm.s.inv(0.15) to solve and get z scores of -1.03643 and 1.281552

now on paper we have 2 equations -1.03=10-mean/standard div and 1.28=20-mean/sd and we can solve them

but how do i use excel to solve this to get the mean and sd for the player. any guidance on how do do this greatly appreciated. my maths is v rusty and any better methods (or correct ones if im wrong) would be great to hear too. im hoping i will be able to get probabilities for say top 30% from this once i have the mean and sd or am i mistaken? thanks in advance

[MrShorty]

my maths is v rusty

Because I find that I do better programming when I have a good handle on the math, I would suggest you loosen up the rusty math, first.

A quick refresher on the algebra of solving systems of linear equations: http://www.purplemath.com/modules/systlin1.htm
In the long run, systems of linear equations are easily solved using matrix algebra: https://www.khanacademy.org/math/pre...ations-systems
Especially when Excel has built in matrix functions like MINVERSE() and MMULT(): https://www.excel-easy.com/examples/...equations.html

From there, multiply everything through by sd (to get sd out of the denominator) and the rest should be as described in the links.

[maxpower2]

hi shorty. i can solve the equations on paper(the simpler stuff still) . i should have been more clear. its just 15 yrs since i did statistics so it was more if the method i was using was correct; given the info available(finding unknown mean and sd etc). and if (assuming finishing position is normal distributed) i can go on to use the estimates for mean and sd to get probabilities for other finishing positions accurately. ie 1st-15th or 1st-40th. i have solved the eq on the spreadsheet now. seems like there could be an easier way tho or a method i may need for harder eq. currently im doing it in bits over numerous cells. will check your links a bit later if thats what they explain. (answered here before checking them. brains bit tired for maths now)