According to the National Center for Health Statistics, the distribution of adult male and female heights is reasonably modeled by a normal density curve. In a 2007 study, the NCHS found that
all adult males (at least 20 years of age) had a mean height of 69.4 inches with a standard
deviation of 2.5 inches. The respective mean and standard deviation for all adult females at
least 20 years of age was 64.8 and 2.2 inches.
(a) Find the z-score and height for someone in the 75th percentile of the height
distribution for adult males.
(b) If an adult female were 66 inches tall, calculate her percentile rank and compare it to
the male in part A.