"Remains Found of Downsized Human Species" reports that "once upon a time, on a tropical island midway between Asia and Australia, there lived a race of little people, whose adults stood just 3.5 feet high."19 The article goes on to tell about the excavation in 2003 of an adult female skeleton, the first of several whose size was small enough to warrant identification as a new human species, called Homo floresiensis after the island of Flores where they were discovered.
a. If heights of adult females today have mean 64.5 inches and standard deviation 2.5 inches, what would be the z-score of a 3.5-foot-tall woman?
b. The article explains that "because the downsizing is so extreme, smaller than that in modern human pygmies, they [scientists] assigned it to a new species." The smallest race of pygmies is said to have an average height of 54 inches. If their standard deviation is about 2 inches, find how many standard deviations below average the Floresian would be compared to pygmies.
c. Do we refer to the standard deviation of all pygmy heights as , x m, s, or s?