# Solve Probability of Distribution

Why does this work:

Solve[Probability[x <= t, x \[Distributed] NormalDistribution[]] == 0.95 ,t]


But this doesn't:

Solve[Probability[x <= t,x \[Distributed] StudentTDistribution[2.964, 2.071, 5]] ==0.95,t]


How can I solve this problem?

• Solve is an exact symbolic solver ... it works mostly with linear equations and polynomials and special cases like the Erf function which it knows how to invert. Since your problem is numerical anyway, try NSolve instead of Solve. Nov 15, 2013 at 13:10
• Same problem with NSolve. Doesn't work. Nov 15, 2013 at 13:28
• Works for me .... what version of Mma are you using? Nov 15, 2013 at 14:16
• Works for me too, but try FindRoot when NSolve doesn't work. FindRoot won't find all roots, just one, but it can handle any "black box" function. Nov 15, 2013 at 23:52

(This may be better as a comment)

This may be an exercise in testing the use of NSolve (which does produce the answer [Version 9]) the normal distribution and StudentTDistribution can be solved with Quantile or InverseCDF, as can be verified by testing solutions.

Quantile[StudentTDistribution[2.964, 2.071, 5], 0.95]


or

InverseCDF[StudentTDistribution[2.964, 2.071, 5], 0.95]


both yielding:

7.13717

• Thank you very much! That helped a lot! Nov 22, 2013 at 10:21