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 2.7

(p. 66). The researchers obtained a random sample of 106 social robots through a Web search and determined that 63 were designed with legs but no wheels.

a. Find a 99% confidence interval for the proportion of all social robots designed with legs but no wheels.
Interpret the result.

b. In Exercise 6.55, you assumed that 40% of all social robots are designed with legs but no wheels. Comment on the validity of this assumption.