7.75 Hard Hats The safety requirements for hard hats worn by construction workers and others, estab- lished by the American National Standards Institute (ANSI), specify that each of three hats pass the following test. A hat is mounted on an aluminum head form. An 4-kilogram (kg) steel ball is dropped on the hat from a height of 1.5 metres, and the resulting force is measured at the bottom of the head form. The force exerted on the head form by each of the three hats must be less than 455 kg, and the average of the three must be less than 386 kg. (The relationship between this test and actual human head damage is unknown.) Suppose the exerted force is normally distributed, and hence a sample mean of three force measurements is normally distributed. If a random sample of three hats is selected from a shipment with a mean equal to 410 and or =45, what is the probability that the sample mean will satisfy the ANSI standard?