Under the system of floating exchange rates, the rate of foreign money to the U.S. dollar is affected by many random factors, and this leads to the assumption of a normal distribution of small daily fluctuations. The rate of U.S. dollar per euro is believed in April 2007 to have a mean of 1.36 and a standard deviation of 0.03.1 Find the following. a. The probability that tomorrow’s rate will be above 1.42. b. The probability that tomorrow’s rate will be below 1.35. c. The probability that tomorrow’s exchange rate will be between 1.16 and 1.23.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Under the system of floating exchange rates, the rate of foreign money to the U.S. dollar is affected by many random factors, and this leads to the assumption of a
a. The probability that tomorrow’s rate will be above 1.42.
b. The probability that tomorrow’s rate will be below 1.35.
c. The probability that tomorrow’s exchange rate will be between 1.16 and 1.23.
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