Instructions: 0 Give only necessary output from Miuitab. You can copy and paste graphs on a Word document. 0 You can choose to hand write or type your solutions. There is a 1 point penalty if the handwritten work is not legible. 0 You need to show your work [formula setup, calculations, etc.) and state any properties or rule: you need to solve the problems to get full credit. I Make sure to follow Gradescope guidelines while making a submission. A penalty of 1 point may be applied if the guidelines are not followed. 1. {6 points} Calculate (by hand} the Five Number Summary and report any outliers for the following data: SCI, 43, 43, 44, 47, 43, 44, 35, 75, 42, 31 2. {5 points) Suppose that scores on a university's entrance exam follow a normal distribution with mean 500 and standard deviation 20. Find the [QR for these scores. 3. {4 points) A dairy farmer has a large herd of cows that produced milk. The farmer knows 10% of the cows produce over 35 liters per day. A business analyst for a local bank was asked to produce a model for the milk production of the farmers herd. He suggested that the milk production for a randomly selected sow from the farmers herd should be normally distributed with a mean 20 liters and standard deviation of 4 liters. Based on what the farmer knows is the business analyst's model appropriate for farmer's herd? Explain your reasoning. 4. {3 points) What are the mean and the median of the uniform distribution given in the gure below? What are the quartiles? Your answer should be based on the properties of density curves and descriptive statistics covered in class. 5. {4 points) High-density lipoprotein (HDL) is sometimes called the \"good cholesterol\" because low values are associated with a higher risk of heart disease. According to the American Heart Association, people over the age of '20 years should have at least 40 milligrams per deciliter {mg/' (:11) of HDL cholesterol. U.S. women aged 20 and over have a mean HDL of 55 rug/ell with a standard deviation of 15.5 mg/dl. Assume that the distribution is Normal. (a) What proportion of women have low values of HDL (40 mgfdl or less}? HDL levels of EU mgjdl and higher are believed to protect people from heart disease. [b] What proportion of women have protective levels of HDL? [c] Women with more than :10 mgfdl but less than 60 mgfdl of HDL are in the intermediate range, neither very good or very bad. What proportion are in this category