Using the TI-84 calculator, find the area under the standard normal curve. Round the answers to four decimal places. (a) Find the area under the standard normal curve that lies outside the interval between z -1.98 and z = 0.61. (b) Find the area under the standard normal curve to the left of z=1.15. (c) Find the area under the standard normal curve to the right of z=1.13. (d) Find the area under the standard normal curve that lies between z=1.67 and z 2.19. 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 481 millimeters with a standard deviation of 41 millimeters. Assume these lengths are normally distributed. (a) What proportion of six-year-old rainbow trout are less than 448 millimeters long? (b) What proportion of six-year-old rainbow trout are between 378 and 478 millimeters long? (c) Is it unusual for a six-year-old rainbow trout to be less than 377 millimeters long? Round the answers to at least four decimal places. A 82 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 485 millimeters with a standard deviation of 45 millimeters. Assume these lengths are normally distributed. Round the answers to at least two decimal places. (a) Find the 35 percentile of the lengths. (b) Find the 74th percentile of the lengths. (c) Find the third 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?