1. Find the critical value to construct a confidence interval at 85%.

For each of the following construct a confidence interval for both 90% and 95%. That means two per problem with the information given.

Problems 2, 3, and 4.

2.) = 31.39, = .80, = 82

3.) From a random sample of 24 months from January 2006 through December 2016, the mean number of tornadoes per month in the United States was about 100. Assume the population standard deviation is 114.

4.) Researchers estimated the mean length of time that the average American spends eating lunch each day. The group takes a random sample of 30 adults and obtains the times listed below. The research council assumes that the population standard deviation is = 6.5

29 12 12 21 23 32 24 26 33 16 24 28 28 28 31

21 18 24 27 29 27 13 32 20 17 13 13 21 17 27

5.) Now with the information giving in Problem #4 find the probability that the average American takes between 19 and 24 minutes to eat lunch. (Hint: This is not a confidence interval around the mean, this is the probability between these two times, think central limit theorem)