The amount of time it takes for a student to complete a stat

The amount of time it takes for a student to complete a statics quiz is uniformly distributed (or, given by a random variable that is uniformly distributed) between 29 and 62 minutes. One student is selected at random. Find the robability of the following events. The student requires more than 56 minutes to complete the quiz Probability = The student completes the quiz in a time between 33 and 40 minutes Probability = The sltudent completes the quiz in exactly 43 26 minutes Probability =

Solution

Let, X follows uniform(29,62)

Then the CDF of X is,

F(x)= (x-29)/(62-29)

a) To find,

P(X>52)= 1-F(52)= 0.4651

b)P(33<X<40)=F(40)-F(33)=0.1667

C) P(X=43.25)=0