A particular professor never dismisses class early Let x den

A particular professor never dismisses class early. Let x denote the amount of time past the hour (minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 min. The density curve is shown in the following figure.

(a) What is the probability that at most 3 min elapse before dismissal?
  

(b) What is the probability that between 3 and 6 min elapse before dismissal?

A particular professor never dismisses class early. Let x denote the amount of time past the hour (minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 min. The density curve is shown in the following figure. (a) What is the probability that at most 3 min elapse before dismissal? (b) What is the probability that between 3 and 6 min elapse before dismissal?

Solution

cumulative distribution of uniform random variable = x-a/b-a

a)

P(X<3) = 3-0/10-0 = 3/10 = 0.3

b)

P(3 < X<6) = P(X<6) - P(X <3)

= 6/10 - 3/10

= 3/10

= 0.3