A bank's loan officer rates applicants for credit. The ratings are normally distributed with a population mean of 200 and a population standard deviation of 50.0. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275. Round your answer to four decimal places.
The diameters of bolts produced by a certain machine are normally distributed with a population mean of 11.0 milimeters (mm) and a population standard deviation of 0.1 mm. Bolts with a diameter less than 10.764 must be discarded. What is the probability that a randomly selected bolt will have a diameter less than 10.764 mm?
