Suppose the amount of time needed to change the oil in a car is uniformly distributed between 14 minutes and 30 minutes, with a mean of 22 minutes and a standard deviation of 4.6 minutes.

Let X represent the amount of time, in minutes, needed to complete a randomly selected oil change. What is the probability that a randomly selected oil change takes at most 20 minutes to complete?

37.5% probability that a randomly selected oil change takes at most 20 minutes to complete.

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.

For this problem, we have that:

Uniformly distributed between 14 minutes and 30 minutes, which means that

What is the probability that a randomly selected oil change takes at most 20 minutes to complete?

This is . So

There is a 37.5% probability that a randomly selected oil change takes at most 20 minutes to complete.

the answer is b

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.