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. the expenditure in town will be normally distributed with mean of 2000
and standard deviation is 500
the range we nhave = (2000-500) to(2000+5000)
=1500 to 2500

since our mean is 2000 i.e the highest probability of meeting the expoenditure of 2000 kronor , we should convert 2000 kronor before leaving

b. we will use z formula here to find the no. of dollars need to convert. we wnat to ensure that there is not more than 1 % chance of non meeting of expenditure or we can say as 99% of probabilty of meeting the expenditure.

we find z value from z table with probability of 99% with single tail i.e 2.33
z= x - xi / s.d
x = desired mean
xi= actual mean of population

s.d =standard deviation
2.33 = (x - 2000)/500

x=3165

so to be 99% of not being out of cash you should have 3165 kronor

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