A man has designed a machine to produce a compound and has calibrated it so the compound always has an atomic weight of 20.4. Unbeknownst to him, the machine has a defect and doesn't always produce a compound with that weight. Assume that the distribution of the weights of the compounds produced by the machine is normal with a mean of 21.37 and standard deviation of 0.4
Suppose 15 compounds are selected independently. What is the P that at most 2 of the compounds have a weight less than 20.857?