Prove that if and then (Lemma 5.1.8).

3.3 Chebyshev’s Rule and the Empirical Rule o Chebyshev’s rule o Empirical rule: For a symmetric (bell shaped) distribution Example : Birth weights of females in the United States (full-term) have a bell-shaped distribution with mean of 7.54 pounds and a standard deviation of 0.61 pounds. Use the empirical rule to answer the following: 68% of U.S. female birth weights are between ________ and __________ 95% of U.S. female birth weights are between ________ and _________. 99.7% U.S. of female birth weights are between _______ and _________. 3.4 The Five-Number Summary; Boxplots To obtain both measures of center and measure of variation. • Quartile Q 1 1 quartile = 25 percentile (median of the part of the entire data set