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

1.975in currency A​ (to currency​ B) and standard deviation

0.034in 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 1.975units 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

More than 2.009 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 1.907units 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

1.888 units of currency A or more than 2.022

units of currency​ A?

Less than 1.888

is more unusual. More than 2.022is more unusual.

Answer 1

X = exchange rate
X = N(1.975, 0.034^2)
a)
P(X > 1.975) = 0.5 = 50 %

b)
P(X > 2.009)
= P(Z > 1)
= (1 - 0.68)/2
= 0.16
= 16 %

c)
P(X < 1.907)
= P(Z < -2)
= ( 1 - 0.95)/2
= 0.025

d)
less than 1.888 = P(Z < -2.55882)
more than 2.022 = P(Z > 1.382353)

since abs (-2.55582) > 1.382353

Less than 1.888 is more unusual