4. 5. (1 point) You are given the monthly house sales in 2013, for istanbul, izmir and the rest of the country. a) Calculate mild and extreme outlier limits for Istanbul, izmir, Rest of Turkey and Total sales. b) Calculate the sample correlation coefficient between sales for (i) Istanbul and izmir, and (ii) Istanbul and the rest of Turkey. c) What do these correlations tell us? Write your answer in the designated range. d) Create a scatter plot of sales in Istanbul versus lzmir. Save the chart as a separate chart sheet, with an appropriate sheet name. Make sure the chart has: 0 Proper axis titles, 0 A proper chart title, 0 No gridlines, o A trendline. (0.6 points) Your aunt owns a small traditional oliveoilbased soap production plant in Northern Aegean region ofTurkey. She is worried that there is a problem with the production process resulting in the weights of the soap bars to be different than what they are supposed to be in the design specications. According to these specifications a soap bar must be 175 i 4 grams. Until recently the production process was "under control" producing soaps whose weight followed the Normal distribution with mean of 175 grams and standard deviation of 1 gram. To help your aunt you took random samples of 10 soaps per day for 5 days. Calculate the following probabilities assuming that the process is under control with mean 175 and standard deviation 1 a) The probability the process produces a bar of soap with weight that is less than or equal to the smallest observed weight for a single soap bar (i.e. an observation]. b} The probability that a sample of 10 soap bars have an average weight (X, read \"Xbar") less than or equal to the smallest observed average weight in those 5 days. c) The probability that the overall average of all the samples (X, read \"Xbar bar") is less than or equal to the overall average you observed for those five days. Since your aunt does not know probability theory you would like to describe what is happening by helping her compare the frequency distributions of the weights of soaps when the process is under control versus how they are distributed now. (:1) Generate 50 random variates that come from the Normal distribution for the process under control (mean 175, standard deviation 1). e] Create two frequency distributions, rst distribution of all 50 observed weights ("actual"), and second for all 50 simulated soap weights, both using the same bin upper limits given. f) You are given the histograms of these two frequency distributions side by side (using the clustered column chart type) as a separate chart sheet. Reduce the gaps between columns to 20%