If z is the positive number such that the interval from z to +

If z is the positive number such that the interval from

μ − zσ to μ + zσ contains 50% of a normal distribution, then

(a) Which percentile is (i) μ + zσ? (ii) μ − zσ?

(b) Find this value of z. Using this result, explain why the upper quartile and lower quartile of a normal distribution are μ + 0.67σ and μ − 0.67σ, respectively.