Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 4.25

(p. 221). The study found that of 106 social robots, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Suppose you randomly select 10 of the 106 social robots and count the number, x, with neither legs nor wheels.

a. Demonstrate why the probability distribution for x should not be approximated by the binomial distribution.

b. Show that the properties of the hypergeometric probability distribution are satisfied for this experiment.

c. Find m and s for the probability distribution for x.

d. Calculate the probability that x = 2.