Question

In: Math

IQ scores have a mean of 100 and standard deviation of 15: a) What percentage of...

IQ scores have a mean of 100 and standard deviation of 15:

a) What percentage of scores fall between 100 & 135?

b) What percentage of scores fall between 88 & 100?

Solutions

Expert Solution

a) What percentage of scores fall between 100 & 135?

X:   IQ score

We apply Z score formula

Now we use TI-83/84 calclator

Follow the path of TI - 83\84

Press " 2ND " ........> Press " VARS" ..........>select "normalcdf"

Lower : 0   ( lower value of Z score )

Upper : 2.333333333

    ( because Z score follows normal distribution with mean 0 and standard deviation 1 )

Now convert that area into percentage .

Percentage of scores fall between 100 & 135 = 0.490184671 * 100 = 49.01846714 %

Here we have not mention any rounding


b) What percentage of scores fall between 88 & 100?

Follow the path of TI - 83\84

Press " 2ND " ........> Press " VARS" ..........>select "normalcdf"

Lower : (-) 0.8    (Note for (-) sign select the sign which is below 3 number key on TI - 84\83)

Upper : 0

Final answer :-

percentage of scores fall between 88 & 100 = 0.2881446669 * 100 = 28.81446669 %

percentage of scores fall between 88 & 100 = 28.81446669 %

Final answer :-

a )

Percentage of scores fall between 100 & 135 = 49.01846714 %

b )

percentage of scores fall between 88 & 100 = 28.81446669 %


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