SOLUTION: A set of data is normally distributed with a mean of 200 and a standard deviation of 50. What percentage of the scores is between 200 and 167? What would be the percentile r

Question 363691: A set of data is normally distributed with a mean of 200 and a standard deviation of 50.
What percentage of the scores is between 200 and 167?
What would be the percentile rank for a score of 176?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A set of data is normally distributed with a mean of 200 and a standard deviation of 50.
What percentage of the scores is between 200 and 167?
z(200) = 0
z(167) = (167-200)/50 = -0.66
P(167< x < 200) = P(-0.66 < z < 0) = 0.2454
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What would be the percentile rank for a score of 176?
z(176) = (176-200)/50 = -0.48
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The percentile rank of a score is the proportion of
population below the score.
%ile of 176 = P(z< -0.48) = 0.3156 = 31.56%ile
Rounding the answer would be 32%ile
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Cheers,
Stan H.

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