Question

5. Suppose that a researcher approximates the density of the CAD/USD exchange rate in January 2018 by ~N(0.75,0.024) (so the mean is 0.75 and the standard deviation is 0.024, measured in US dollars). (a) Find the probability of observing an exchange rate less than 0.762. (b) Find the probability of observing an exchange rate between 0.75 and 0.78 (c) Find a value m such that 0.75 + m > z > 0.75-rn 95% of the time. (d) Find a value m such that 0.75 +m > x > 0.75-m 99% of the time.

Answer 1

a)

X = N(0.75,0.024^2)

P(X < 0.762)

= P(Z <(0.762 - 0.75)/0.024)

= P(Z < 0.5 )

= 0.6915

b)

P(0.75 <X< 0.78)

= P ( 0<Z<1.25 )

=0.3944

c)

m is z * sd

z = 1.96 for 95 %

= 1.96 * 0.024

= 0.04704

d)

z = 2.576 for 99 %

m = 2.576 * 0.024

= 0.061824