Question 1192634
.
The movie Forrest Gump, the public school required an IQ of at least 80 for admittance. 
IQ test scores are normally distributed with mean 100 and standard deviation 16
(a) What percentage of people would qualify for admittance to the school.
(b) If the public school wishes 95 percent of all children to qualify for admittance, 
what minimum IQ test score should be required for admittance?
~~~~~~~~~~~~~~~~~~~~~~~~~~



            The solution and the answer for part  (b) 

            in the post by  @PChill both are  INCORRECT.



<pre>
His error is that he interprets 95%, or 0.95, as the area on the LEFT of the row mark,
while, in reality, 95%, or 0.95, is the area on the RIGHT of the row mark.


    +--------------------------------------------------+
    |   Indeed, they want to take 95% among the best   |
    |       - - - not 95% among the worst !            |
    +--------------------------------------------------+



The right answer is that the required IQ for part (b) is 73.6823.


To learn the subject better, go to web-site 

https://onlinestatbook.com/2/calculators/inverse_normal_dist.html

and play there with free of charge online calculator.



Print the parameters in the calculator's window  Area = 0.95, mean = 100, SD = 16
and specify the option "Above".  


The calculator will give you the answer immediately and will show the area of interest.
</pre>

Solved correctly for part (b).

 
After playing with this calculator 5 - 10 - 15 minutes, you will learn the subject
and will know it better than if 7 or 15 best teachers will explain to you during a semester.



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