The amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 30 and 60 minutes. The professor wants to reward (with bonus marks) students who are in the lowest quarter of completion times. What completion time should he use for the cutoff for awarding bonus marks

37.5 minutes

Step-by-step explanation:

Let the amount of time it takes a student to complete a statistics quiz be = t

t is uniformly distributed between 30 minutes and 60 minutes

The professor wants to reward with bonus marks, students who are in the lowest quarter of t

- What value of t should he use as the cutoff for awarding bonus marks?

A quarter of any number is 1/4 of it.

Now, the range of t (the difference between the highest and lowest values of t) is 60 - 30 = 30

1/4 of 30 = 7.5

The lowest quarter of t is hence between 30 and 37.5

So the cutoff for awarding bonus marks is t = 37.5minutes

INTERPRETATION:

Any student who spends 37.5 minutes or below on a statistics quiz, will be awarded bonus marks.

Step-by-step explanation:

the 2nd line can be rewritten as y < x-3

So, any value that is less than both 4x+4 and x-3 will work

Pick any value you want for x, and figure y possibilities

x=0; x-3=-3, 4x+4=4, so y<-3 ... (0,-5) will work

I'm sure you can now come up with other pairs.