Suppose x is a random variable best described by a uniform probability distribution with c=20 and d=40.
find the probability p(20≤x≤35).

P(20≤x≤35) = 0.75 .

Step-by-step explanation:

We know that the probability distribution function of Uniform Distribution is represented as :

     If x follows Uniform(c,d) then,

          f(x) = where c < x < d

To fond the given probability it is better to first calculate the Cumulative Distribution Function(CDF) of Uniform Distribution.

The CDF of Uniform Distribution is P(X<=x) = where d > c .

Therefore, P(20<=x<=35) = P(x<=35) - P(x<20)

  P(x<=35) =    because we are given c = 20 and d = 40.

                 = = 0.75

 P(x<20) =    = = 0

Hence, P(20<=x<=35) = 0.75 - 0 = 0.75.