Hints and/or comments about Problem 22

• You can start by finding the inverse cdf (with pencil and paper), and use it to determine the 10th and 90th percentiles of the logistic distribution in closed form (as opposed to using statistical software to get values which have been rounded (although statistical software could be used to check your inverse cdf). But then I think you'll find that it's best to make use of something like Maple or Mathematica (or I guess anything that can do numerical integration) for the integration.
• For part (b) you may run into trouble if you try to set the derivative of an expression equal to 0 and solve. If so, you should be able to use graphics to help search for the desired value, and perhaps finish off by printing values corresponding to various trimming proportions in order to make sure that you get 3 accurate significant digits.
• One of the tables in the handouts that I'll distribute on July 9 (that pertain to an overhead projector presentation that I give in STAT 554) ought to be useful for determining whether you are in the "right ballpark" (but to get 3 accurate significant digits, you'll have to carefully grind through the calculus (hopefully using appropriate software)).