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# Brand Brewery PercentAlcohol Calories Carbohydrates American Amber Lager Straub Brewery 4.10 136 10.5 American Lager Straub Brewery 4.10 132 10.5...

- 1. The website beer100.com advertises itself as “Your Place for All ThingsBeer.” One of their “things” is a list of 153 domestic beer brands with thepercent alcohol, calories per 12 ounces, and carbohydrates per 12 ounces.(a) The figure below gives a scatterplot of carbohydrates versus percentalcohol. Give a brief summary of what can be learned from the plot.(b) One of the points is an outlier. Please identify this point and explain why itis an outlier.2. Use the attached beer dataset for the following problems(a) The outlier identified in Problem 1 has been removed from the beer data.Generate a scatterplot of the percent alcohol and carbohydrates for the152 domestic beer brands.(b) Calculate the correlation between percent alcohol and carbohydrates.3. Use the attached beer dataset for the following problems(a) Fit a Least-Square Regression line by using percent alcohol to predictcarbohydrates and write down the regression equation. (Use the formulasfor ????" and ????#)(b) Based on the regression line above, can you predict how manycarbohydrates (per 12 ounces) are there in a beer containing 7% alcohol?4. Decay of a radioactive element. Barium-137m is a radioactive form of theelement barium that decays very rapidly. It is easy and safe to use for labexperiments in schools and colleges. In a typical experiment, the radioactivityof a sample of barium-137m is measured for one minute. It is then measuredfor three additional one-minute periods, separated by two minutes. So thedata are recorded at 1, 3, 5 and 7 minutes after the start of the first countingperiod. The measurement units are counts. Here are the data for one of theseexperiments:Time 1 3 5 7Count 578 317 203 118(a) Using the least-squares regression equationCount = 602.8 – (74.7 * time)and the observed data above, find the residuals for the counts.(b) Plot the residuals versus time.Now use the log counts data:Time 1 3 5 7Log Count 6.35957 5.75890 5.31321 4.77068(c) Using the least-squares regression equationLog Count = 6.593 – (0.2606 * time)and the observed data above, find the residuals for the counts.(d) Plot the residuals versus time.5. Eight is enough. A health body needs good food, and healthy teeth areneeded to chew our food so that it can nourish our bodies. The U.S Army hasrecognized this fact and requires recruits to pass a dental examination. If youwanted to be a soldier in the Spanish American War, which took place in1898, you needed to have at least eight teeth. A study reported the rejectiondata for enlistment candidates classified by age. Here are the data:AGE (YEARS)REJECTED Under 25 25-35 Over 35YES 715 2897 6688NO 136876 99591 87554(a) Find the joint distribution.(b) Find the two marginal distributions.(c) Find the conditional distribution of Rejected given Age.