The amount of time it takes Emma to wait for the train is continuous and uniformly distributed between 4 minutes and 11 minutes. What is the probability that it takes Emma more than 5 minutes to wait for the train?

85.71% probability that it takes Emma more than 5 minutes to wait for the train

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

Uniformly distributed between 4 minutes and 11 minutes.

This means that .

What is the probability that it takes Emma more than 5 minutes to wait for the train?

Either it takes 5 or less minutes, or it takes more than 5 minutes. The sum of the probabilities of these events is 1. So

We want to find . So

85.71% probability that it takes Emma more than 5 minutes to wait for the train

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus