According to a report by the U.S. Fish and Wildlife Service, the mean length of six-year-old rainbow trout in the Arolik River in Alaska is 477 millimeters with a standard deviation of 37 millimeters. Assume these lengths are normally distributed.

(a) Find the 48th percentile of the lengths.

(b) Find the 81st percentile of the lengths.

(c) Find the first quartile of the lengths.

(d) A size limit is to be put on trout that are caught. What should the size limit be so that 15%

of six-year-old trout have lengths shorter than the limit?

Round the answers to at least two decimal places.