3. The random variable \(X\) has a continuous uniform distribution on \([ a , b ]\) where \(a\) and \(b\) are positive numbers.
Given that \(\mathrm { E } ( X ) = 23\) and \(\operatorname { Var } ( X ) = 75\)
- find the value of \(a\) and the value of \(b\).
Given that \(\mathrm { P } ( X > c ) = 0.32\)
- find \(\mathrm { P } ( 23 < X < c )\).