Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, The researchers obtained a random sample of 106 social robots through a Web search and determined the number that were designed with legs, but no wheels. Let p̂ represent the sample proportion of social robots designed with legs, but no wheels. Assume that in the population of all social robots, 40% are designed with legs, but no wheels.
a. Give the mean and standard deviation of the sampling distribution of p̂.
b. Describe the shape of the sampling distribution of p̂.
c. Find P(p̂ > .59).
d. Recall that the researchers found that 63 of the 106 robots were built with legs only. Does this result cast doubt on the assumption that 40% of all social robots are designed with legs, but no wheels? Explain.