Question

In a standardized IQ test the mean score is 100 and the standard deviation is 15. according to the empirical rule, 95% of all those who took the test should have scores between

Answer 1

The empirical rule is a statistical rule which states that for a normal distribution, almost all data will fall within three standard deviations of the mean. Broken down, the empirical rule shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the distribution's average.

So,

Upper limit = Mean + 2*Standard deviation = 100 + 2*15 = 100 + 30 = 130

Lower limit = Mean - 2*Standard deviation = 100 - 2*15 = 100 - 30 = 70

Hence,

According to the empirical rule, 95% of all those who took the test should have scores between 70 and 130