Probability question --> Gaussian Random Variables

[9danny]

I'm stuck. Any hints will be greatly appreciated.
"The summer temperature in town can be modeled as a Gaussian Random Variable T (in degree Farenheit). It has been observed that the T<= 95 occurs with a probability of 0.8413, and that T<=100 occurs with a probability of 0.97725. What is the mean and variance of T?"
If P[T<= 95] = 0.8413 --> Φ(z) = 0.8413 --> z =1 (from CDF table). At same time
P[T <=100] = 0.97725 --> Φ(z) = 0.97725 --> z = 2
How come I have two different z? What formula can I use to solve for the mean and the variance? z = (x - mean) / σ but since I have two different z and two different values for x, which one is the one to use? I get two different values for the mean.
(I know that Var[x] = σ2, so I need to find σ).
PLEASE HELP!

 

[marcmtlca]

An observation

You seem to have done most of the work.

I will simply point out that you have two equations and two unknowns. This is usually a good thing!!!

\(\displaystyle 1=\frac{95-\mu}{\sigma}\)

and

\(\displaystyle 2=\frac{100-\mu}{\sigma}\)