Question

If the mean and standard deviation of a continuous random variable that is normally distributed are 28 and 3 respectively using the empirical rule find an interval that contains 95% of the distribution

Answer 1

Approximately 95% of the measurements will fall within 2 standard deviations of the mean, i.e. within the interval (µ − 2σ, µ + 2σ):

$(\mu-2\sigma, \mu+2\sigma)=(28-2\cdot3, 28+2\cdot3)=(22,34).$ .