An important measure of the performance of a locomotive is i

An important measure of the performance of a locomotive is its \"adhesion,\" which is the locomotive\'s pulling force as a multiple of its weight. The adhesion of one 4400-horsepower diesel locomotive model varies in actual use according to a Normal distribution with mean = 0.4 and standard deviation = 0.044

What proportion of adhesions (± 0.001) measured in use are higher than 0.46?  

What proportion of adhesions (± 0.001) are between 0.46 and 0.48?  

Solution

Normal Distribution
Mean ( u ) =0.4
Standard Deviation ( sd )=0.044
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 0.46) = (0.46-0.4)/0.044
= 0.06/0.044 = 1.3636
= P ( Z >1.364) From Standard Normal Table
= 0.0863                  
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 0.46) = (0.46-0.4)/0.044
= 0.06/0.044 = 1.3636
= P ( Z <1.3636) From Standard Normal Table
= 0.91366
P(X < 0.48) = (0.48-0.4)/0.044
= 0.08/0.044 = 1.8182
= P ( Z <1.8182) From Standard Normal Table
= 0.96548
P(0.46 < X < 0.48) = 0.96548-0.91366 = 0.0518