1. The tensile strength of a certain type of wire is normally distributed with a mean of 98.5 and a standard deviation of 10.8. If you draw a sample of size eighty-one from this population, what is the probability that the sample mean tensile strength will be between 96.5 and 100.5?

2. A doctor wishes to develop an interval estimate for scores on a patient questionnaire. She wants the interval to be within 5 points with a 99% confidence level. She does not know the standard deviation, but in previous years the scores have ranged from 48 to 97. How large a sample should she draw?