1. The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. Based on a large number of observations, the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation of 11.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?
2. Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes, and the population standard deviation of this distribution is 15 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the probability that the mean time for the sample of 170 returns is between 88 minutes and 92 minutes?
3. The weight of trucks traveling on a particular section of I-475 has a population mean of 15.8 tons and a population standard deviation of 7.2 tons. What is the probability a state highway inspector could select a sample of 50 trucks and find the sample mean to be 14.3 tons or less?