In: Statistics and Probability
Fish story: 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) What proportion of six-year-old rainbow trout are less than 440 millimeters long?
(b) What proportion of six-year-old rainbow trout are between 370 and 470 millimeters long?
(c) Is it unusual for a six-year-old rainbow trout to be less than 371 millimeters long?
Round the answers to at least four decimal places.