Researchers obtained a random sample of 1114 social robots through a Web search and determined the number that were designed with legs, but no wheels. Letp 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 :1 below. a. Give the mean and standard deviation of the sampling distribution of p. The mean is. (Round to four decimal places as needed.) The standard deviation is. (Round to four decimal places as needed.) b. Describe the shape of the sampling distribution of p. Choose the correct answer below. O A. The sampling distribution is skewed right. O B. The sampling distribution is uniform. O C. The sampling distribution is exactly normal. O D. The sampling distribution is bimodal. O E. There is not enough information given to determine the shape of the sampling distribution. O F. The sampling distribution is approximately normal. O G. The sampling distribution is skewed left. c. Find P (p > 0.57) . P (p> 0.57) =[ (Round to four decimal places as needed.) 42 d. The researchers found that 63 of the robots were built with legs only. Does this result cast doubt on the assumption that % of all social robots are designed with legs, but no wheels? Explain. Let probabilities less than 0.05 be significantly small and probabilities greater than 0.95 be significantly large. 63 The proportion _ is approximately equal to so this result doubt on the assumption. If it were true that 41% of all social robots are designed with legs, the probability that 63 or more robots in a sample of + +robots are built with legs only is which is 104