6) An industrial oven used to cure sand cores for a factory manufacturing engine blocks for small cars is able to maintain fairly constant temperatures. The temperature range of the oven follows a normal distribution with a mean of 450F and a standard deviation of 25F. Leslie Larsen, president of the factory, is concerned about the large number of defective cores that have been produced in the past several months. If the oven gets hotter than 450F, the core is defective.

a) What is the probability that the oven will cause a core to be defective?

b) What is the probability that the temperature of the oven will range from 470F to 475F?