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Finding a value given a proportion

# Finding a value given a proportion - E X A M P L E 3.9Find...

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Finding a value given a proportion EXAMPLE 3.9 Find the top 10% using software Scores on the SAT reading test in recent years follow approximately the  (504,111)  distribution . How high must a student score in order to place in the top  10% of all students taking the SAT? We want to find the SAT score  x  with area 0.1 to its  right  under the Normal curve  with  mean   μ  = 504 and  standard deviation   σ  = 111. That’s the same as finding  the SAT score  x  with area 0.9 to its  left.   Figure       3.12      poses the question in  graphical form. Most software will tell you  x  when you plug in  mean  504,  standard deviation  111, and cumulative proportion 0.9. Here is Minitab’s output: Minitab gives  x  = 646.252. So scores above 647 are in the top 10%. (Round up  because SAT scores can only be whole numbers.)

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Figure       3.12
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Finding a value given a proportion - E X A M P L E 3.9Find...

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