SOLUTION: The average score on the math portion of the SAR was 516 in 2002. Suppose that the math scores of all students taking the SAT in 2002 were normally distributed with a mean of 516 a

Question 1201333: The average score on the math portion of the SAR was 516 in 2002. Suppose that the math scores of all students taking the SAT in 2002 were normally distributed with a mean of 516 and a standard deviation of 90.
i. What percentage of the students scored higher than 600 on this exam?
ii. An elite technical college requires a student’s math SAT score to be 700 or higher to be considered for admission. What percentage of the students who look the SAT in 2002are eligible for consideration by this college?
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
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The average score on the math portion of the SAR was 516 in 2002.
Suppose that the math scores of all students taking the SAT in 2002 were normally distributed
with a mean of 516 and a standard deviation of 90.
(a) What percentage of the students scored higher than 600 on this exam?
(b) An elite technical college requires a student’s math SAT score to be 700 or higher
to be considered for admission. What percentage of the students
who look the SAT in 2002are eligible for consideration by this college?
~~~~~~~~~~~~~~~~~~~

(a)  You are given a normal curve with the mean value of 516 and the standard deviation of 90.

     They want you determine the area under this normal curve on the right of the raw score z=600.

     You may use the standard function normalcdf on your calculator TI-84

                        z1    z2  mean SD   <<<---=== formatting pattern
         P = normalcdf(600, 9999, 516, 90).


         +-------------------------------------------------------------------+
         |  normalcdf stands for "normal cumulative distribution function".  |
         +-------------------------------------------------------------------+


     You will get the number P = 0.1753.  So, your ANSWER to question (a) is 17.53%.


     If the meaning of this procedure is still unclear to you, then go to web-site

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

     and use free of charge online calculator there, which is intended for the same purposes.

     This online calculator has perfect and intuitively clear interface, so even a beginner student 
     can use it without any difficulties.  Surely, this online calculator will get you the same answer.
     The calculator shows the area of the interest, so after using it, you will understand the meaning 
     of the procedure in full.



(b)  This time they want you determine the area under the same normal curve on the right
     of the raw mark z=700.

     Again and similarly, you may use the standard function normalcdf on your calculator TI-84

                        z1    z2  mean SD   <<<---=== formatting pattern
         P = normalcdf(700, 9999, 516, 90).


     You will get the number P = 0.0205.  So, your ANSWER to question (b) is 2.05%.


     You may repeat the same procedure as above with the online calculator to better adopt/master the procedure.
     At the end, you will get the same answer.

Solved.

---------------

Using this online calculator is priceless/invaluable helper/teacher in mastering this technology.

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