Problem 08 Archaeology: Tree Rings [4 points] calculator At Burnt Mesa Pueblo, the method of tree-ring dating gave the following years for an archaeological excavation site (Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo, edited by Kohler, Washington State University): 1189 1271 1267 1272 1268 1316 1275 1317 1275 (a) Assuming that the variable x is normally distributed, find the 90% confidence interval for u = the mean tree- ring date from this archaeological site. answer to the nearest year Calculator Function Used: Calculator Inputs: sequence must be correct Calculator Answer: (b) Interpretation: What does the confidence interval mean in the context of this problem? How valid is this conclusion for archaeological sites in general?Problem 06 Meteorology: Confirmation of Normal Distribution [7 points] calculator The following problem is based on information from the National Oceanic and Atmospheric Administration (NOAA) Environmental Data Service. Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in July in the town of Kit Carson, Colorado. NOAA has stated that the x distribution for Colorado has a mean / of approximately 75.F and standard deviation o of approximately 8 F. A 20-year study (630 July days) of town temperature records gave the entries in the rightmost column of the following table. Observed Region Under Expected Percentage Normal Curve from Normal Curve 1 x u+ 30 0.15% Use a 1% level of significance to test the claim that the average daily July temperature follows a normal distribution with u = 75 F and o = 8'F. use integers throughout your calculations show your work (a) Calculator Function: V: test statistic value: p-value: (b) Conclusion and interpretation in terms of this problem.Problem 07 Insurance: Satellites [7 points] cateutntnr A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a u = 90 months and a a" = 3.7 months. When this computer relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for $50 million. Assume that the only part of the satellite in question is the microchip. All other components will work indenitely. answer to the nearest cent Show your work (a) If the satellite is insured for 84 months, what is the expected loss to the insurance company? (b) If the insurance company charges $3 million for 34 months of insurance, how much prot does the company expect to make