The mean weight of all Goliath grouper caught on the Treasure coast is 408 pounds, with a standard deviation of 65 pounds. Suppose a random sample of 49 Goliath grouper from the Treasure Coast are caught and weighed.

This question asks to determine the probability that the average weight of the sample of 49 Goliath Grouper is within 11 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast. Round the solution to 4 (four) decimal places, if necessary. P (x within 11 pounds of u)= ____. May I have all the relevant instructions to solve this problem? Step-by-step if possible? Thank you.