Let H be the head circumference. Z = (H – μ) / σ, is the standard normal.

Find P( 21.6 < H < 24 ) = P((21.6 - μ) / σ < Z < (24 - μ) / σ) = P((21.6 - 22.8) / 1.2 < Z < (24 - 22.8) / 1.2) = P(-1 < Z < 1 ) = 68% The 68 - 95 - 99.7 "rule" would be that: P( -1 < Z < 1) = 0.68 ie the prob that a normal random variable is within 1 standard deviation of the mean is 68% P( -1.96 < Z < 1.96) = 0.95 ie the prob that a normal random variable is within 1.96 standard deviation of the mean is 95% P( -2.97 < Z < 2.97) = 0.997 ie the prob that a normal random variable is within 2.97 (many times rounded to 3) standard deviation of the mean is 99.7%