what percent of these differ from the population mean(nomal distribution)

Question

if a set of observations is normally distributed, what percent of these differ from the population mean by more than 0.96σ, where σ is the population standard deviation.

Answer 1

by the empirical rule, 68% fall within 1 standard deviation of the mean. That means 100%-68% are outside of 1 standard deviation or 32%

.96 is almost 1. So the number that fall outside of 0.96 standard deviation is slightly more than 32%

for a more accurate less approximate percentage, use z tables or a calculator with statistics functions.

the empirical rule says 68% all within one standard deviation, 95% fall within 2 standard deviations and 99% fall within 3 standard deviations. it's the 68-95-99 rule for 1,2 and 3 standard deviations from the mean