Use the empirical rule.

Question

Scores on an IQ test for people aged 20-34 are normally distributed with a mean of 110 and a standard deviation of 25. What percent of people in the age group have scores above 160?

Answer 1

The empirical rule is a shorthand way to determine percentages of the scores within 1, 2 and 3 standard deviations from the mean of a normal distribution. It's called the 68-95-99.7 rule. 68% of the scores will be within 1 standard deviation from the mean, or from 85 to 135. 110-25=85. 110+25=135. 95% within 2 standard deviations, from 60 to 160. 99.7% within 3 standard deviations, from 35 to 185. 160 minus 110 = 50. 50 = 2 standard deviations from the mean of 110. That means 95% of the scores are between 60 and 160. 110-50=60 110+50=160. The remaining 5% of the scores are above 160 or below 60. half of 5% is above 160, or 2.5%. The other half of 5% are below 60 or 2.5%. So the answer is 2.5%. 97.5% of the test scores are below 160. 95% +2.5%=97.5%.