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standardizing a distribution / Jm Check Your Understanding: 1. According to an article on Yahoo! news, you should change your sheets every 7 days. To investigate the sheet changing habits of adults, a random sample of 20 adults were given an anonymous survey. Here is a dotplot and summary statistics of the results. n mean SD min Q1 med max 20 30 40 50 60 70 80 90 100 110 120 20 42.75 34.984 15 21 30 60 120 Time before changing sheets (days) a. Suppose you convert the time before changing sheets from days to weeks. Describe the shape, mean, and standard deviation of the distribution of time before changing sheets in weeks. b. The adults in the study are given an article explaining the health benefits of changing the sheets more often. After reading the article each person agrees to change their sheets one week earlier than they did before. How does the shape, mean, and standard deviation of this distribution compare with the distribution of time in part (a)? c. Now suppose you convert the time before changing sheets from part (b) to z-scores. What would be the shape, mean, and standard deviation of this distribution