(Show Work) Assume that): is normally distributed with mean 20 and standard deviation 2. Determine the following: a. P{X 13} c. P{18 x) = 0.9??2 (Show Work) The length of an injected-molded plastic case that holds tape in normally distributed with mean length 90.2 mm and a standard deviation of 0.1 mm. e. What is the probability that a part is shorter than 90.3 mm and longer than 89.? mm? f. What should the process mean be to obtain the greatest number of parts between 89.? and 90.3 mm? g. If parts that are not between 89.? and 90.3 mm are scrapped, what is the yield of the process mean that you chose in part b DASL displays a histogram of chest sizes of 457 men in the Scottish army in the early 18005. See the file ch estut for the data. a. Use the data given to create a histogram. Based on the plot, does the data seem follow a normal distribution? b. Now use a probability plot to decide if the data follows a normal distribution Compute the mean and standard dEviation of the data d. Using yourestimates, and assuming that the data does follow a normal distribution, what percent of men do you expect to have chests biggerthan 43 inches? What percent actually do? e. Based on your answers to part d, do you believe that the data comes from a normal distribution? Why or why not? P