Question

Suppose x is a random variable best described by a uniform probability distribution with c=20 and d=40.

Answer 1

Answer:

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) = $\frac{1}{d-c}$ 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) = $\frac{x-c}{d-c}$ where d > c .

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

  P(x<=35) =  $\frac{x-20}{40-20}$  because we are given c = 20 and d = 40.

                 = $\frac{35-20}{40-20}$ = 0.75

 P(x<20) =  $\frac{x-20}{40-20}$  = $\frac{20-20}{40-20}$ = 0

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