Waist circumference of women in their twenties follows a somewhat normal distribution with mean 32 inches, standard deviation 5 inches.
a. Use the 68-95-99.7 Rule to sketch a histogram for a large data set of women's waist circumferences, marking off the circumferences that are within 1, 2, and 3 standard deviations of the mean.
b. Sketch a normal curve for the waist circumferences of all women.
c. Approximately what is the percentage of waists that are larger than 42 inches?
d. The smallest 16% of waists are less than how many inches?
e. More precisely, the mean for women in their twenties is 32.2, and their median is 30.6. The mean for women in their eighties is 36.7, and their median is 36.4. Which age group has more skewness in the distribution of waist circumferences?
f. Is the skewness observed in part (e) left or right?