Waist circumference of women in their twenties follows a somewhat normal distribution with mean 32 inches, standard deviation 5 inches.
a. How do we denote the number 32?
b. How would we denote the mean waist circumference for a sample of women in their twenties?
c. The mean, 32 inches, is actually just an estimate made by researchers. Is it closer to the truth if it was based on information from a well-designed study of 1,000 women, or of 10,000 women, or doesn't it matter?
d. How many standard deviations away from the mean is a waist circumference of 32?
e. If the z-score for a woman's waist circumference is 2.4, should we report it to be somewhere in the top 50%, the top 16%, the top 2.5%, or the top 0.15%?
f. If the z-score for a woman's waist circumference is 2.4, would we consider it to be fairly common, unusually small, or unusually large?
g. Find the waist circumference for a woman whose z-score is 2.4.
h. Find the waist circumference for a woman whose z-score is 1.2.