Answer to Question #151153 in Statistics and Probability for Alex

Question

if the mean and the standard deviation of a continuous random variable that is normally distributed are 26 and 6, find an interval that contains 95% of the distribution

Answer 1

According to the empirical rule:

95% fall within two standard deviations.

$= 26 ± 2 \times 6 \\ = 26 ± 12 \\ = (26-12, 26+12) \\ = (14, 38)$