IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
a. what percent of IQ scores are between 85 and 115?

Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
a. what percent of IQ scores are between 85 and 115?

pphalke · Answer

how do I go about doing that step @welshfella

welshfella · Answer

sorry i messed up there
its been a long time.

pphalke · Answer

hey that's ok this standard deviation is new to me we never got taught this

welshfella · Answer

find the z scores first 

z1  =  85 - mean / STD DEV  =  85-100 /  15  =  -1


can you find the z score for  IQ of 115?

welshfella · Answer

same method as for z1


z2  = (115 -100 )/ 15   =  ?

welshfella · Answer

Oh - talking to myself again!

pphalke · Answer

sorry was writing it down and for z2 I got 1

pphalke · Answer

@welshfella

welshfella · Answer

thats correct  

now we find the area under the standard normal curve  between  z =  -1 and  1 from   the tables.
Tgis is given as a fraction so we need to  convert to a percentage.

welshfella · Answer

have you got normal distribution tables?

welshfella · Answer

in this case its the area between - 1 and 1  so look up the value for 1 and multiply it by 2.

pphalke · Answer

so I would look up that how?

welshfella · Answer

I guess you can find it online or in a math or statistics textbook

welshfella · Answer

OK heres a link But this table gives the area to the left of the z scores So you need to note the values in the table for -1 and 1 and subtract value for z = -1 from value for z = 1. http://math.arizona.edu/~rsims/ma464/standardnormaltable.pdf

welshfella · Answer

OK I'll read the  value for z = 1

it is  0.84134

can you find the value for  z =-1?

welshfella · Answer

(There's different variations of the standard normal curve )

Always read  the instructions on the top of the graph before you use it.

pphalke · Answer

I am looking at that graph

welshfella · Answer

Its just a matter of finding -1.0 in the first (Z) column and reading the next number on its right.

pphalke · Answer

I see .15866 for the number to the right of 1.0

welshfella · Answer

correct 
so the required  percentage is  ( 0.84134 - 0.15866) * 100

welshfella · Answer

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pphalke · Answer

68%

welshfella · Answer

thats the area we require

which is the area from left side of curve to  z=1  - area from left side z = -1

welshfella · Answer

68% is correct

68 .27 to be more exact

welshfella · Answer

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