Question

The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable that is uniformly distributed) between 25 and 59 minutes. One student is selected at random. Find the probability of the following events.

A. The student requires more than 54 minutes to complete the quiz.
Probability =

B. The student completes the quiz in a time between 30 and 35 minutes.
Probability =

C. The student completes the quiz in exactly 43.78 minutes.
Probability =

Answer 1

here for uniform distribution parameter a =25 and b=59

a)

P(X>54)=1-P(X<54)=1-(54-25)/(59-25)=0.1471

b)

P(30<X<35)=(35-30)/(59-25)=0.1471

c)

P(X=43.78 ) =0 (since on a continuous distribution , point probability of an event is 0)