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 1.444 in currency A (to currency B) and standard deviation 0.047 in currency A Given this model, and using the 68-95-99 7 rule to ate 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 1.444 units of currency A? The probability is %. 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 less than 1.350 units of currency A? The probability is %. (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 1.397 units of currency A? The probability is %. (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 1.355 units of currency A or more than 1.494 units of currency A? More than 1.494 is more unusual. Less than 1.355 is more unusual.

Explanation / Answer

a) P(X > 1.444)

= P(z > (1.444 - 1.444)/0.047)

= P(z > 0)

= 0.5

= 50%

b) P(X < 1.350)

= P(z < (1.350 - 1.444)/0.047)

= P(z < -2)

= 0.025

= 2.5%

c) P(X < 1.397)

= P(z < (1.397 - 1.444)/0.047)

= P(z < -1)

= 0.16

= 16%

d) Less than 1.355 is more unusual. Option B is correct.

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