The external diameter of a part is known to be normally distributed with a mean of 40 mm and standard deviation of 2.5 mm. The specications on the diameter are (36, 45), which means that part diameters between 36 and 45 mm are considered acceptable. The unit cost of rework is $0.20, while the unit cost of scrap is $0.50. (Rework is done if the outside diameter is greater than 45 mm and the gear assembly is scrapped when the outside diameter is less than 36 mm). The daily production rate is 2000 items.

a) What is the the probability of scrap? (Express in 4 decimal places).

b) What is the probability of rework? (Express in 4 decimal places).

c) What is the cost of scrap? ($ XX.XX)