Researchers obtained a random sample of 110 social robots through a Web search and determined the number that were designed with legs, but no wheels. Let p^ represent the sample proportion of social robots designed with legs, but no wheels. Assume that in the population of all social robots, 42% are designed with legs, but no wheels. Complete parts a through d below.

a. Give the mean and standard deviation of the sampling distribution of p^.

b. Describe the shape of the sampling distribution of p^

c. Find P(p^ > .59)

d. Recall that the researchers found that 63 of the 110 robots were built with legs only. Does this result cast doubt on the assumption that 42% of all social robots are designed with legs, but no wheels? Explain.