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 30 and 58 minutes. one student is selected at random. find the probability of the following events.
(a) the student requires more than 52 minutes to complete the quiz.
(b) the student completes the quiz in a time between 36 and 41 minutes.
(c) the student completes the quiz in exactly 42.63 minutes.

Using the uniform distribution, it is found that there is a:

a) 0.2143 = 21.43% probability that the student requires more than 52 minutes to complete the quiz.

b) 0.1786 = 17.86% probability that the student completes the quiz in a time between 36 and 41 minutes.

c) 0% probability that the student completes the quiz in exactly 42.63 minutes.

Uniform probability distribution:

An uniform distribution has two bounds, a and b.  

In this problem, the distribution is uniformly distributed between 30 and 58 minutes, thus: .

Item a:

The probability is:

0.2143 = 21.43% probability that the student requires more than 52 minutes to complete the quiz.

Item b:

The probability is:

0.1786 = 17.86% probability that the student completes the quiz in a time between 36 and 41 minutes.

Item c:

The probability of an exact value is 0, thus 0% probability that the student completes the quiz in exactly 42.63 minutes.

A similar problem is given at link

Let denote this random variable. Then

a.

b.

c.

∞ this is your sign

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.