Difficult# Waldo's Bags of Candy

APSTAT-PX4EOJ

Snack-sized bags of fruit-flavored candy are manufactured so that the weights are nearly normally distributed with a mean of $64$ grams and a standard deviation of $1.5$ grams. It is reasonable to assume that the bags are packaged randomly for shipment to stores.

Waldo purchased $12$ snack-sized bags of this fruit-flavored candy and found that the average weight of these bags was $63$ grams.

Does Waldo have reason to believe he was cheated?

Calculate the probability of obtaining a sample mean less than or equal to $63$ grams.