# Help normal distribution maths q

Help with this question I don’t get it I got these for the z values
(edited 1 year ago)
Original post by vc94

I don’t know how to work it out
Your working has 1-Mu = -1.405 x sigma and 5-Mu= 1.0803 x sigma
Solve simultaneously for Mu and sigma.
But you got Mu=3.26 which I agree with, your sigma is wrong I believe.
Original post by vc94
Your working has 1-Mu = -1.405 x sigma and 5-Mu= 1.0803 x sigma
Solve simultaneously for Mu and sigma.
But you got Mu=3.26 which I agree with, your sigma is wrong I believe.

The one on the whiteboard is my working the other one is the markscheme (sigma is 1.61 I wrote it wrong by accident from ms)
But my whiteboard method why is it incorrect ??
(edited 1 year ago)
Okay, so how did you get your 2 z-values?
Original post by vc94
Okay, so how did you get your 2 z-values?

Well,
Z~N(0,1^2)
For the p(x<1) it’s a left tail and 0.08 for the area and I put all that in my calculator (graphical) to get the value for Z
Same for the other z value
P(X<1) is a probability from the distribution X~N( Mu, variance) with the unknown parameters.
When you standardise X, you get
P(Z < (1 - mu) / sigma )) =0.08 which is from the distribution Z~N(0, 1^2) .... so you can use the inverse normal function on this which leads to
(1 - mu) / sigma = -1.405
(edited 1 year ago)