An apple juice producer buys all his apples from a conglomer

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.
What is the probability that a randomly selected apple will contain between 2.00 and 3.00 ounces?

Solution

Normal Distribution
Mean ( u ) =2.25
Standard Deviation ( sd )=0.15
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 2) = (2-2.25)/0.15
= -0.25/0.15 = -1.6667
= P ( Z <-1.6667) From Standard Normal Table
= 0.04779
P(X < 2.15) = (2.15-2.25)/0.15
= -0.1/0.15 = -0.6667
= P ( Z <-0.6667) From Standard Normal Table
= 0.25249
P(2 < X < 2.15) = 0.25249-0.04779 = 0.2047