(35 pts) We are interested in fitting a distribution to historical gym-membership durations. Attached is a list of membership start and end dates that started in 2006. HINT: Excel can "subtract" dates; if you subtract the start date from the end date you will get the duration of the subscription measured in days. Using a Q-Q plot, compare the fit for the following two distributions. Comment (in a couple of sentences) on how well the distributions fit the data. (1) A Normal distribution with density f(x) = 1 2 e 1 2 ( x ) 2 ( < x < ) and parameters = 170.79 and = 92.51; and (2) A Log-Normal distribution with density f(x) = 1 x 2 exp( (ln x) 2 22 ) (x > 0) and parameters = 5.01 and = 0.51. Note: You must provide and clearly explain the detailed calculations used to generate the Q-Q plots. HINT: NORM.INV and LOGNORM.INV functions in Excel return the inverse c.d.f. of the Normal and Log-Normal distributions, respectively