1. Using Seligman’s assumptions, calculate the probability that a single adult Chinese man, chosen at random, will be less than or equal to 5 feet tall, or equivalently, 60 inches tall.

2. Do the results in part 1 agree with Seligman’s odds?

3. Comment on the validity of Seligman’s assumptions. Are there any basic flaws in his reasoning?

4. Based on the results of parts 1 and 3, do you think that Deng Xiaoping took height into account in selecting his successor?

If you were the boss, would height play a role in your selection of a successor for your job? In his Fortune column, Daniel Seligman discussed his ideas concerning height as a factor in Deng Xiaoping’s choice of Hu Yaobang as his replacement as Chairman of the Chinese Communist Party.12 As Seligman notes, the facts surrounding the case arouse suspicions when examined in the light of statistics.

Deng, it seemed, was only 5 feet tall, a height that is short even in China. Therefore, the choice of Hu Yaobang, who was also 5 feet tall, raised (or lowered) some eyebrows because, as Seligman notes, “the odds against a ‘height-blind’ decision producing a chairman as short as Deng are about 40 to 1.” In other words, if we had the relative frequency distribution of the heights of all Chinese men, only 1 in 41 (i.e., 2.4%) would be 5 feet tall or shorter. To calculate these odds, Seligman notes that the Chinese equivalent of the U.S. Health Service does not exist and hence that health statistics on the current population of China are difficult to acquire. He says, however, that “it is generally held that a boy’s length at birth represents 28.6% of his final height” and that, in prerevolutionary China, the average length of a Chinese boy at birth was 18.9 inches. From this, Seligman deduces that the mean height of mature Chinese men is

18.9/.286 = 66.08 inches, or 5 feet 6.08 inches

He then assumes that the distribution of the heights of men in China follows a normal distribution (“as it does in the U.S.”) with a mean of 66 inches and a standard deviation equal to 2.7 inches, “a figure that looks about right for that mean.”