You are traveling abroad and have only American dollars with you. You are currently in the capital but you will soon be heading out to a small town for an extended stay. In the town, no one takes credit cards and they only accept the domestic currency (shillings). In the capital, you can convert dollars to shillings at a rate of two shillings per dollar. In the town, you learn that one dollar only buys 1.6 shillings. Upon your return to the capital at the end of your trip, you can convert shillings back to dollars at a rate of 2.5 shillings per dollar. You estimate that your expenditures in the town will be normally distributed with mean of 400 shillings and standard deviation of 100 shillings.
a. How many dollars should you convert to shillings before leaving the capital?
b. After some thought, you feel that it might be embarrassing if you run out of shillings and need to ask to convert additional dollars, so you really do not want to run out of shillings.
How many dollars should you convert to shillings if you want to ensure there is no more than a 1 in 200 chance you will run out of shillings?