Problem 1. A meteorologist who sampled 13 thunderstorms found that the average speed at which they traveled across a certain state was 15 miles per hour. The standard deviation of the sample was 1.7 miles per hour. Find the 99% confidence interval of the mean.


Problem 2.  A sample of 400 people are given a drug, and 278 report that their symptoms are relieved. Find a 90% confidence interval for the true proportion of the population who experience relief of symptoms due to this drug.


Problem 3.  A new drug has been developed for a group of people and the researchers are worried that it might have an effect on pulse rate. A sample of 36 people taking this experimental drug is taken from the population. The mean pulse rate of the sample is 84 bpm with a standard deviation of 5 bpm. Find a 92% confidence interval for the true mean pulse rate of people taking the experimental drug.