Fluctuations in the exchange rate of dollars against the pou

Fluctuations in the exchange rate of dollars against the pound sterling over a short time period were approximated by a normal distribution with a mean of 3.20 and a standard deviation of 0.2. What is the probability that the rate on a particularly day was more than 3.05?

Solution

Normal Distribution
Mean ( u ) =3.2
Standard Deviation ( sd )=0.2
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 3.05) = (3.05-3.2)/0.2
= -0.15/0.2 = -0.75
= P ( Z >-0.75) From Standard Normal Table
= 0.7734