The amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following events. a. The student requires more than 55 minutes to complete the quiz.
b. The student completes the quiz in a time between 30 and 40 minutes.
c. The student completes the quiz in exactly 37.23 minutes.

a) 0.1667 = 16.67% probability that the student requires more than 55 minutes to complete the quiz.

b) 0.3333 = 33.33% probability that the student completes the quiz in a time between 30 and 40 minutes.

c) 0% probability that the student completes the quiz in exactly 37.23 minutes.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.  

The probability of finding a value of at lower than x is:

The probability of finding a value between c and d is:

The probability of finding a value above x is:

Uniformly distributed between 30 and 60 minutes.

This means that

a. The student requires more than 55 minutes to complete the quiz.

0.1667 = 16.67% probability that the student requires more than 55 minutes to complete the quiz.

b. The student completes the quiz in a time between 30 and 40 minutes.

0.3333 = 33.33% probability that the student completes the quiz in a time between 30 and 40 minutes.

c. The student completes the quiz in exactly 37.23 minutes.

Probability of an exact value in a continuous distribution, such as the uniform distribution, is 0%, so:

0% probability that the student completes the quiz in exactly 37.23 minutes.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet