Question

Let X be normally distributed with mean and variance.
a) Verify that q3 = mean + 0.67σ and that q1 = mean - 0.67σ.
b) Find the interquartile range for X.
c) Verify that the inner fences for X are f1 = mean - 2.68σ and f3 = mean + 2.68σ.
d) Verify that the probability that X will fall beyond the inner fences is approximately 0.007.