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Scores on the SAT form a normal distribution with a mean of µ = 500 with...

Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100. If the state college only accepts students who score in the top 85% on the SAT, what is the minimum score needed to be accepted? Group of answer choices 396 604 525 475

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Answer #1

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A top 85% means the minimum score to be within the top 85%. Please check the wording of the question as it asks to get the minimum score to be in the top 85%, and not 15%, so we must find value "c" such that P(X>c) = .85

We are given params of normal dist:

Mean = 500

Stdev = 100

Standardizing using the above params:

P(Z> (c-500)/100 ) = .85

This can be written as :

P(Z<= (c-500)/100) = 1-.85 = .15

Looking at Z-tables a cumulative probability of .15 has a Z score of -1.0364

So, (c-500)/100 = -1.0364

c = -1.0364*100+500 = 396.36, rounding off : 396

Answer: 396

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