Check Your Understanding: According to an article on Yahoo!news, you should change your sheets every 7 days.. .at minimum. To investigate the sheet changing habits of adults, a random sample of 20 adults reported how often they change their sheets using an anonymous survey. Here is a dotplot and summary statistics of the results. 20 30 40 50 60 70 80 90 100 110 120 Time before changing sheets (days) n mean SD min Q1 med Q3 max 20 42.75 34.984 15 21 30 60 120 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 that would arise from changing their sheets more often. After reading the article each person agrees to change their sheets one week sooner than they used to. How does the shape, center, and variability 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? Explain your answers. STATS MED