Find the probability that a student finishes in less than 5 mins. Draw & shade the distribution to interpret your results

Question

time it takes for 20 students to finish this quiz is uniformly distributed from 0 mins to 15 mins. 

Answer 1

Hello Ariel G.,

You have sent in 3 questions about the same thing. I will tell you how to do the first one.

In each case, you want to figure out what fraction of the total time they are asking about. The total time is 15 minutes (0 to 15). Students who finish in less than 5 minutes are between 0 and 5 which is 5 minutes.

So the probability is 5 minutes out of 15 or 5/15 = 1/3. You can do this because a uniform distribution means the times are perfectly evenly distributed.

(In a real test, this does not happen. A fast student might finish in 5 or 6 minutes, and most of the students might take 12 to 15 minutes so they would not be evenly distributed among the times from 0 to 15.)