empirical rule for mean of 166 standard deviation of 8 aproxment percentages for 150 and 182 and also 142 and 190

Question

I have a mean of 166. the standard deviation is 8. Need approximate percentage between the following values 150 and 182 and  142 and 190 using the empriical rule

Answer 1

The empirical rule is a rule-of-thumb guide to evaluating percentages associated with z-scores, for normal distribution.

|z|=1, 68%; |z|=2, 95%; |z|=3, 99%.

For the given numbers the z-scores are:

150: (150-166)/8=-2

182: (182-166)/8=2

142: (142-166)/8=-3

190: (190-166)/8=3

So for 150 and 182 the empirical rule the percentage is 95%; for 142 and 190 it's 99%.