Use the Central Limit Theorem to Find Probabilities Round ea…

Use the Central Limit Theorem to Find Probabilities Round each probability to 4 decimal places.  The mean weight of adult males in the United States is 184 pounds with a standard deviation of 32 pounds. Find the probability of randomly selecting 49 adult males with a mean weight greater than 190 pounds.  Why are we allowed to use the central limit theorem in this case?