2. Scores on the Mathematics section of the SAT Reasoning Test form a normal distribution with a mean of µ = 100 and a standard deviation of σ = 100.
a. If the state college only accepts students who score in the top 60% on this test, what is the minimum score needed for admission?
b. What is the minimum score necessary to be in the top 10% of the distribution?
c. What scores form the boundaries for the middle 50% of the distribution?
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Answer:
by trial and error:
a. 126
score -> percentile
100 -> 0.5
125 - > 0.59871
126 -> 0.60257
b.
300-> 0.97725
240-> 0.91924
235 -> 0.91149
230 -> 0.9032
229 -> 0.90147
228 -> 0.89973
c. 33 and 168
25th & 75th percentile
33 -> 0.25143
168 -> 0.75175