A shipment of steel bars will be accepted if the mean breaking strength of a random sample of 6 steel bars is greater than 245 pounds per square inch. In the past, the breaking strength of such bars has had a mean of 236 and a variance of 408. (Round your answers to four decimal places.)
(a) Assuming that the breaking strengths are normally distributed, what is the probability that one randomly selected steel bar will have a breaking strength in the range from 241 to 252 pounds per square inch?
(b) What is the probability that the shipment will be accepted?