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Snowcat [4.5K]
3 years ago
11

The SAT Reasoning Test (formerly called the Scholastic Aptitude Test) is perhaps the most widely used standardized test for coll

ege admissions in the United States. Scores are based on a normal distribution with a mean of 1500 and a standard deviation of 300. Clinton College would like to offer an honors scholarship to students who score in the top 10 percent of this test. What is the minimum score that qualifies for the scholarship?
Minimum Score:
Mathematics
1 answer:
slamgirl [31]3 years ago
6 0

Answer:

The score is  x  =  1884

Step-by-step explanation:

From the question we are told that

     The population mean is  \mu  = 1500

     The standard deviation is  \sigma  =  300

     

From the question we are told that the score follow a normal distribution

i.e     X  \~  \   N( 1500 , 300)

The proportion of score in the top 10% is mathematically

           P(X > x )  =  P( \frac{X -  \mu}{\sigma }  > \frac{x -  \mu}{\sigma }   ) = 0.10

Where x is the minimum score required to be in the top 10%

Now the \frac{X -  \mu}{\sigma }   =  Z (The  \ Standardized \ value \  of  \  X)

  So

            P(X > x )  =  P( Z > \frac{x -  \mu}{\sigma }   ) = 0.10

So

            P(X > x )  =  P( Z > \frac{x -  1500}{300}   ) = 0.10

So the critical value of  0.10  from the normal distribution table is  Z_{0.10} =  1.28

So

               \frac{x -  1500}{300}   = 1.28

              x  =  1884

           

       

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