A shipment of steel bars will be accepted if the mean breaking strength of a random sample of 10 steel bars is greater than 250 pounds per square inch. In the past, the breaking strength of such bars has had a mean of 235 and a variance of 400.
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 245 to 255 pounds per square inch?
b. What is the probability that the shipment will be accepted?