A set of sofa prices are normally distributed with a mean of 2500 dollars and a standard deviation of 200 dollars.
A leather sofa has a price of 2410 dollars.
What proportion of sofa prices are higher than the price of the leather sofa?
You may round your answer to four decimal places.

We have been given that a of sofa prices are normally distributed with a mean of 2500 dollars and a standard deviation of 200 dollars.  A leather sofa has a price of 2410 dollars. We are asked to find the proportion of sofa prices that are higher than the price of the leather sofa.

First of all, we will find the z-score corresponding to sample score 2410.

Now we need to find area under normal curve that is greater than z-score of that is .

Using formula , we will get:

Now we will find area under curve using normal distribution table.

Upon rounding to 4 decimal places, we will get:

Therefore, approximately 0.6736 of sofa prices are higher than the price of the leather sofa.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s