1. For problems 1a through 1.b, assume that the length of a population of fish is normally distributed with population mean = 63 cm and population standard deviation = 9 cm. 1.a What proportion of the individual fish are longer than 76 cm? 1.b What proportion of the fish are between 42 and 84 cm long?

2. For problem 2.a through 2.c, assume that a population of automobile engines has a population mean useful life = 120,000 miles and population standard deviation = 8400 miles. Also assume the data is normally distributed.

2.a What proportion of the engines last more than 140,000 miles? 2.b What proportion of the engines last between 110,400 to 130,600 miles? 2.c The manufacturer wants to write a warranty so that only 0.8% (0.008) of the engines fail while under warranty. For how long should the warranty be written?

3. Use the following data for problems 3.a, 3.b, 3.c, and 3.d The time required to wait for service at a government office is normally distributed. It has population mean = 40 minutes with population standard deviation = 8 minutes. 3.a What proportion of wait times are more than 54 minutes? 3.b What proportion of the wait times are less than 36 minutes? 3.c What proportion of the wait times are between 34 to 46 minutes? 3.d What is the 80th percentile (P80)? You are encouraged (but not required) to round to the nearest whole percentile.