# Find z-score?

GROUPS:
 Hello, everyone. I know how to calculate the probability with Mathematica: Probability[ x >= 1.0, x ~ NormalDistribution[] ] The answer is 0.158655.My question is, how can I find the z-score of normal distribution when the probability is given? For example, I want to find the value of z in the below pseudo-code: Probability[ x >= z, x ~ NormalDistribution[] ] == 0.05 Or is there any ready-made function that can compute z-score directly in Mathematica? Thank you!
10 days ago
4 Replies
 Mariusz Iwaniuk 2 Votes By numeric:  NSolve[Probability[x >= z, x \[Distributed] NormalDistribution[]] == 5/100, z, Reals] (* {{z -> 1.64485}} *) By symbolic:  Solve[Probability[x >= z, x \[Distributed] NormalDistribution[]] == 5/100, z] // Quiet (* {{z -> Sqrt[2] InverseErfc[1/10]}} *) 
 Michael Rogers 3 Votes Also InverseCDF[]: InverseCDF[NormalDistribution[], 0.95] (* 1.64485 *) InverseCDF[NormalDistribution[], 95/100] (* Sqrt[2] InverseErfc[1/10] *)