Aset of test scores is normally distributed with a mean of 145 and a standard deviation of 11. seif received a score of 167. what was his percentile score

97.5%

84%

95%

63.5%

Since , which means the corresponding z-score for Seif's test score is . The empirical rule asserts that for any normal distribution, approximately 95% of it lies within two standard deviations of the mean, i.e. , which leaves 5% outside of that range, and specifically 2.5% to either side.

This means



In other words, a test score of 167, which corresponds to a z-score of 2, marks the 97.5th percentile.