The daily exchange rates for the five-year period 2003 to 2008 between currency

Question

The daily exchange rates for the five-year period 2003 to 2008 between currency A and currency B are well modeled by a normal distribution with mean 1.057 in currency A (to currency B) and standard deviation 0.034 in currency A Given this model, and using the 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more precisely, complete parts (a) through (d) a) What is the probability that on a randomly selected day during this period, a unit of currency B was worth more than 1.057 units of currency A? The probability is 11% (Type an integer or a decimal.) b) What is the probability that on a randomly selected day during this period, a unit of currency B was worth more than 1.159 units of currency A? The probability is 11% Type an integer or a decimal.) c) What is the probability that on a randomly selected day during this period, a unit of currency B was worth less than 1.023 units of currency A? The probability is 11% Type an integer or a decimal.) d) Which would be more unusual, a day on which a unit of currency B was worth less than 1.018 units of currency A or more than 1.101 units of currency A? O More than 1.101 is more unusual. O Less than 1.018 is more unusual.

Explanation / Answer

a) probability =50% (as it is in mid)

b)as 1.159 is 3 std deviation away;

P(Z>3) =0.15%

c)as 1.023 is 1 std deviation below mean

P(Z<1)=16%

d)as 1.101 is far away from mean than 1.018

hence more than 1.101 is more unusual

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