"Suppose exam scores are normally distributed with a mean of 70 and a standard deviation of 6. The probability that someone scores between a 70 and a 90 is:"

The probability is 0.40824

Step-by-step explanation:

To find this probability, we shall start with finding the z-scores of each

Mathematically;

z-score = (x-mean)/SD

for 70

z = (70-70)/6 = 0

For 90

z = (90-70)/6 = 20/6 = 10/3 = 1.33

So the probability we want to find is;

P(0 < x < 1.33)

we can use the standard normal distribution to get this;

Mathematically, that would be;

P( x <1.33) - P( x < 0)

Using the standard normal distribution table, we have;

P = 0.40824

answer: 298143

step-by-step explanation:

-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