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.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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