4. The continuous random variable \(X\) is uniformly distributed over the interval \([ \alpha , \beta ]\) Given that \(\mathrm { E } ( X ) = 3.5\) and \(\mathrm { P } ( X > 5 ) = \frac { 2 } { 5 }\)

1. find the value of \(\alpha\) and the value of \(\beta\) Given that \(\mathrm { P } ( X < c ) = \frac { 2 } { 3 }\)
2. 1. find the value of \(c\)
   2. find \(\mathrm { P } ( c < X < 9 )\) A rectangle has a perimeter of 200 cm . The length, \(S \mathrm {~cm}\), of one side of this rectangle is uniformly distributed between 30 cm and 80 cm .
3. Find the probability that the length of the shorter side of the rectangle is less than 45 cm .