Answer:
a) 95% of people has an IQ score between 76 and 124.
b) 0.3% of people has an IQ score less than 64 or greater than 136.
c) 0.15% of people has an IQ score greater than 136
Explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 100
Standard deviation = 12
(a) What percentage of people has an IQ score between 76 and 124?
76 = 100 - 2*12
124 = 100 + 2*12
So within 2 standard deviations of the mean, and the percentage is 95%.
(b) What percentage of people has an IQ score less than 64 or greater than 136?
64 = 100 - 3*12
136 = 100 + 3*12
99.7% of people has scores between 64 and 136. So 100 - 99.7 = 0.3% of people has an IQ score less than 64 or greater than 136.
(c) What percentage of people has an IQ score greater than 136?
0.3% of people has an IQ score less than 64 or greater than 136.
Since the normal distribution is symmetric, 0.3%/2 = 0.15% are below 64 are 0.15% are above 136.