Question

If a population has a mean of 101 and a standard deviation of 7.5, where precisely, does the Empirical Rule state that 95% of the observation/data lie? 2) If you are in the 80th percentile on a standardized test, explain what this means. DId you score 80% on the test?

Answer 1

Empirical rule states that 95 % of the observation/data lies between 2 standard deviations of the mean, that is,

Mean - 2*Standard Deviation = 101 - 2 * 7.5 = 101 - 15 = 86

Mean + 2*Standard Deviation = 101 + 2 * 7.5 = 101 + 15 = 116

So, 95 % of the observation/data lies between 86 and 116

If you are in the 80^th percentile on a standardized test, it means that your score is greater than 80% of the scores of people taking the test.