Question

SAT scores were originally scaled so that the scores in each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Use the empirical rule to estimate the probability that a randomly-selected student gets a section score higher than 600.

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Answer 1

A normal distribution with a mean of 500 and a standard deviation of 100.

To find the probability that a randomly-selected score higher than 600 (P>600), we first find the z-score.

z = (value - mean)/SD = (600 - 500)/100 = 1

Check the table of z-score cumulative normal distribution, we found:

P(z<1) = 0.84134

=> P(> 600) = 1 -0.84134 = 0.15866 = ~16%

Hope this helps!

:)

Answer 2

D. 16%

Explanation:

Find the z-score

z = (600-500)/100 = 1

P(z < 1) = 0.8413

P(> 600) = 1 -0.8413 = 0.1587 × 100

15.87%