The average weight of a professional football player in 2009 was 257.4 pounds. Assume the population standard deviation is 35 pounds. A random sample of 31 professional football players was selected. Complete parts a through e. a. Calculate the standard error of the mean. .com/Student/Player NE I Round to two decimal places as needed) b. What is the probability that the sample mean will be less than 249 pounds? P (x <249) (Round to four decimal places as needed) c. What is the probability that the sample mean will be more than 242 pounds? P(x>242)- Round to four decimal places as needed.) d. What is the probability that the sample mean will be between 262 pounds and 269 pounds? P (262 sx s 269) Round to four decimal places as needed.) e. Identify the symmetrical interval that includes 95% of the sample means if the true population mean ection 7.4 ional football player in 2 selected. Complete pa the mean. s needed.) is 257 4 pounds (Round to the nearest pound as needed)