I really need help with this math problem. I'm sooo frustrated!!!?

Question

IN a normal distribution with the mean being 72 and the standard deviation 12. Beyond what scores do the most extreme 10% lie?

Please explain to me how to do it...Don't just give me an answer..

thank you soooo much!!!

Answer 1

You need to understand Z scores.  You should have a table that gives the Z score for different values on the normal distribution.  Often the table has a picture along with it so you know what  the percent refers to.  

The Z score is just the # of standard deviations to give you a certain proportion of the population.  Usually the table will be one sided or two sided (it's drawn as a curve with a filled-in portion and a tail missing--the missing tail is the percent you're looking for).  That is important for your question.  If you are wondering only what the LARGEST 10% of the population is, you need a 1 sided table.  But if you are asking the most extreme 10%, that is the LARGEST 5% and the SMALLEST 5%.  That table has two tails on either side.  

If you are just looking for the LARGEST 10%, you may have to look up on the one-sided table for where the value of the table is .9 (all full except for the the last 10% or .1 is empty under the curve) and find the Z score.   Then you use the formula that connects the Z score to the population value, the standard deviation and the mean, and solve for the population value.  

Because the table is symmetric, if you only have one-sided or two-sided tables, you can figure out the other side.  For example, 10% on both sides, is equivalent to 5% on one side.

Answer 2

normal distribution refers to a gaussian curve. The mean is 72 refers to the average score.  That means that most people recieved a scor of 72, and this is the tallest part in the center of the curve. Stadard deviation allows you to devide the curve up in a manageable way.  For example, plus or minus 1 standard deviation (72+12=84, 72-12=60) accounts for 68% of the scores.  In other words, all scores between 60 and 84 accound for 68% of all scores.  Likewise, plus or minus 2 standard deviations (72+24=96, 72-24=48) will encompass 95% of scores.  So, all scores between 48 and 96 includes 95% of all the scores recorded.  Your question asks you about the most extreme 10%, so you must apply a standard deviation range that will encompass 90% of all the scores recorded.  You will then be able to find the range of scores as I explained above.  Hope I helped.