(Example 3.7) The National Collegiate Athletic Association (NCAA) uses a sliding

Question

(Example 3.7) The National Collegiate Athletic Association (NCAA) uses a sliding scale for eligibility for Division I athletes. Those students with a 2.5 high school GPA must score at least 820 on the combined mathematics and critical reading parts of the SAT to compete in their first college year. The combined scores of the almost 1.7 million high school seniors taking the SAT in 2013 were approximately Normal with mean 1011 and standard deviation 216. What percent of seniors score at least 820 (+/-0.1)? Use Table A to find your answer. %

Explanation / Answer

Normal Distribution
Mean ( u ) =1011
Standard Deviation ( sd )=216
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 820) = (820-1011)/216
= -191/216= -0.8843
= P ( Z <-0.8843) From Standard Normal Table
= 0.1883                  
P(X > = 820) = (1 - P(X < 820)
= 1 - 0.1883 = 0.8117                  

81.17% are socre atleast 820

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