You are traveling abroad and have only American dollars with you. You are curren

Question

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 (krona) In the capital, you can convert dollars to kronor at a rate of 8.3 kronor per dollar. In the town, you learn that one dollar only buys 6.5 kronor. Upon your return to the capital at the end of your trip, you can convert kronor back to dollars at a rate of 12.5 kronor per dollar. You estimate that your expenditures in the town will be normally distributed with mean of 2000 kronor and standard deviation of 500 kronor. (a) How many kronor should you convert to before leaving the capital? (b) After some thought, you feel that it might be embarrassing if you run out of kronor and need to ask to convert additional dollars, so you really do not want to run out of kronor. How many dollars should you convert to kronor if you want to ensure there is no more than a 1 in 100 chance you will run out of kronor?

Explanation / Answer

a)

Expenditures in the town are normally distributed.

Mean of 2000 kronor and standard deviation of 500 kronor.

No of kronor should be converted = mean + std deviation

i.e., 2000+500 = 2500 kronor

should be converted before leaving the capital at the rate of 8.3 kronor per dollar.

b)

If do not want to get into situation where need to convert additional dollar to kronor so that no more than 1 in a 100 chance will run out of kronor is mean + 3*std deviation.

i.e., 2000+ 3*500=2000+1500=3500 kronor

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