WILL FAN AND MEDAL
The grades on the last art exam had a mean of 75%. Assume the population of grades on art exams is known to be distributed normally, with a standard deviation of 7%. Approximately what percent of students earn a score between 75% and 82%?
37.2%
84.1%
34.1%
50%

- anonymous

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- Hayleymeyer

ohh snap, these problems! X_X

- anonymous

I know that i need to use the z-Score formula, But now when it says "between %75 and %82"
ZSCORE = \[z= \frac{ \mu - x }{ }\]

- anonymous

whoops theres supposed to be a sigma under that

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## More answers

- Hayleymeyer

hmmm

- Hayleymeyer

@pooja195 help please? im not very good with this stuff! :)

- Hayleymeyer

@Luigi0210 :)

- Hayleymeyer

yay!! help has arrived!

- Luigi0210

Don't know much stats, sorryy
@imqwerty

- Hayleymeyer

qwerty, you better help this kid! :)

- imqwerty

damn this is statistics!!!

- Hayleymeyer

@graysongraddylol do you still need help? :)

- anonymous

Yes I do @Hayleymeyer

- Hayleymeyer

okay, ima find you some help, cuz you seem nice

- Hayleymeyer

@phi

- anonymous

thank you :)

- Hayleymeyer

anytime!

- Hayleymeyer

@Nnesha

- anonymous

@phi

- anonymous

@freckles

- phi

mean of 75%.
standard deviation of 7%
score between 75% and 82%?
(it is a bit confusing because our measurements are percents (on a test)... and we also have percent (under a curve) )
but we want the area under the bell curve from 75% (the mean) and 82% (which is 1 std dev to the right of the curve)
how much area is between the mean and 1 std dev from the mean
do you know how to figure that out ?

- anonymous

i have no clue what a standard deviation is :(

- Hayleymeyer

yay! you got help!!

- phi

do you know what a bell curve looks like?

- anonymous

Like this.?
|dw:1440706033076:dw|

- phi

yes. and its symmetric (left side looks like right side)
the exact middle is the mean

- anonymous

|dw:1440706112012:dw|

- anonymous

|dw:1440706140992:dw|

- phi

the idea is the "area under the curve" is set = to one
btw, in theory the "tails" never reach the x-axis
half of the area is below the mean, and 1/2 of the area is above the mean

- anonymous

Can't I solve this using the z-score formula.?

- phi

yes, we use z-scores. But you need to get the basic ideas
so far, you know (for example)
|dw:1440706289865:dw|

- anonymous

A friend of mine just told me it was 34.1% is that correct.?

- phi

a "standard deviation" is a way to measure how far we are away from the mean
you should memorize
the area from -1 std dev (below the mean) to 1 std dev (above the mean)
is 68.27% of the entire area

##### 1 Attachment

- anonymous

That is the emperical rule, Correct.?

- phi

in other words, you should know this
|dw:1440706585153:dw|

- phi

there is a mathematical definition of the curve, and you can calculate the area.
In the real world, measurements (for example, height of people), will form an almost perfect bell curve, and we can use the math to closely model the real world.
back to your problem
75 is the mean
82 is 1 std dev above the mean
we want this area
|dw:1440706762063:dw|

- phi

you are told the area from -1 to +1 is 68.27%
your know the area is symmetric about the mean (in other words, 1/2 of that 68.27 is on the left side and 1/2 is on the right side of the mean)
that is enough info to figure out how much area is from 0 to 1 (it's 1/2 of the area from -1 to 1)

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