Solved: Uniform Distribution The reaction time X (in

Answer:

Step 1

Uniform Distribution The reaction time X (in minutes) of a certain chemical process follows a uniform probability

distribution with 5 ≤ X ≤ 10.

(a) The graph of the density curve is as follows

(b) We take X to be the angle at which the pointer comes to rest, so we use the interval

[5, 10] = [a, b]  as its range. Since all angles are equally likely, the probability density function should not depend on x and therefore should be constant. That is, we take f  to be uniform f(x)=

The probability that the reaction time is between 6 and 8 minutes is

Now, P(6 X 8)

P(cXd)= Area of shaded rectangle ==