Statistics Algebra 2 help !

- anonymous

Statistics Algebra 2 help !

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- anonymous

The grades on the last science exam had a mean of 89%. Assume the population of grades on science exams is known to be distributed normally, with a standard deviation of 14%. Approximately what percent of students earn a score between 75% and 89%?

- anonymous

Help please @jim_thompson5910 @amistre64 @Mertsj @SolomonZelman @iGreen @jdoe0001 @Nnesha @e.mccormick @Loser66 @Luigi0210 @ash2326 @surjithayer @KyanTheDoodle @oldrin.bataku @JoannaBlackwelder @Lady.Liv1776 ???

- amistre64

hmm, id have to know what your material has covered so far

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## More answers

- amistre64

and what you have to work the problem with

- amistre64

it feels to me like an empirical rule approximation tho ...

- anonymous

it is indeed, but im not sure how to use it

- amistre64

well, determine how many deviations are between the mean and your end points

- amistre64

what is our mean?

- anonymous

89%

- amistre64

and what is our left end point?

- anonymous

75%

- anonymous

with a standard deviation of 14%

- amistre64

so, the difference between them is:
what is 89-75?

- anonymous

14

- amistre64

which is exactly 1 standard deviation to the left of the mean. right?

- amistre64

if we calculate the same with the other end point .. well, 89 to 89 is a difference of 0, so no standard deviations are to the right of the mean.
what are your thoughts?

- anonymous

I didnt get it, can you elaborate more?

- amistre64

the only thing left to elaborate is what does the empirical rule state?
it may be called something else in your material tho.

- amistre64

and do we have options to choose from?

- anonymous

68% will fall within the first standard deviation, 95%, the first two and 99.7 first three

- anonymous

the options are:
38.5%
15.7%
50%
34.1%

- amistre64

thats the rule yes, but it is better stated:
within +- 1sd from the mean falls 68% of the data.
68/2 = 34
so 34% to the left (-1 sd), and 34% to the right (+1 sd)
we know we are 1sd to the left, and 0 to the right ...
what does that tell us?

- amistre64

|dw:1437697237025:dw|

- anonymous

I'm lost on this....

- amistre64

it as plain as i can make it, you will have to tell me where it is losing you at.

- anonymous

"within +- 1sd from the mean falls 68% of the data.
68/2 = 34
so 34% to the left (-1 sd), and 34% to the right (+1 sd)
we know we are 1sd to the left, and 0 to the right ...
what does that tell us?"

- anonymous

I dont know what "that tell us"

- amistre64

we determined how many standard deviations we are to the left of the mean, didnt we?
89-75 = ??

- anonymous

14

- amistre64

14 is the difference between the mean and the endpoint, and our standard deviation has a length of 14.
what is 14/14?

- anonymous

1

- amistre64

so we are 1 sd to the left of the mean with that calculation.
using the rule that you stated, or rather that i stated better:
within +- 1sd from the mean falls 68% of the data.
68/2 = 34
so 34% to the left (-1 sd), and 34% to the right (+1 sd)
we know we are 1sd to the left ... which gives us a value of ????

- anonymous

ohh ok I think I get it

- anonymous

the answer would be 34% of the students will get between 75 and 89

- amistre64

we are 0 to the right of the mean so there is nothing to concern ourselves with over on that side ... so all in all, what would you say the answer chould be?

- anonymous

34.1%

- amistre64

thats what I would go with as well :)

- anonymous

got it right thanks

- amistre64

good luck

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