The weights of produced by company are normally distributed

The weights of produced by company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.4 occurs. What is the probability that a randomly selected item from the production will weigh between 4.64 and 4.9 ounces?

Solution

Mean ( u ) =4.5
Standard Deviation ( sd )=0.4
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 4.64) = (4.64-4.5)/0.4
= 0.14/0.4 = 0.35
= P ( Z <0.35) From Standard Normal Table
= 0.63683
P(X < 4.9) = (4.9-4.5)/0.4
= 0.4/0.4 = 1
= P ( Z <1) From Standard Normal Table
= 0.84134
P(4.64 < X < 4.9) = 0.84134-0.63683 = 0.2045