1. A random sample of 100 is taken from a population with a mean of 140 and standard deviation of 25. What is the probability that the sample mean lies between 138 and 142?
2. A manufacturer wants to state a specific guarantee for the life of a product with a replacement for failed products. The distribution of lifetimes of the product has a mean of 1000 days and standard deviation of 150 days. What life length should be stated in the guarantee so that only 10% of the products need to be replaced?