Question 37: The distribution of SAT scores is normal with a mean of µ = 500...

Question 37:

The distribution of SAT scores is normal with a mean of µ = 500 and a standard deviation of σ = 100.

What SAT score (i.e., X score) separates the top 25% of the distribution from the rest?

What SAT score (i.e., X score) separates the top 40% of the distribution from the rest?

What SAT score (i.e., X score) separates the top 4% of the distribution from the rest?

Solutions

Expert Solution

Let the random variable X denote the distribution of SAT scores. Now, we are given that:

Part 1

Let 'a' denote SAT score which separates the top 25% of the distribution from the rest. Thus, 'a' satisfies:

Part 2

Let 'b' denote SAT score which separates the top 40% of the distribution from the rest. Thus, 'b' satisfies:

Part 3

Let 'c' denote SAT score which separates the top 4% of the distribution from the rest. Thus, 'c' satisfies:

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orchestra answered 1 year ago

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