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 = 0.033

What proportion of adhesions (± 0.001) measured in use are higher than 0.4?    

What proportion of adhesions (± 0.001) are between 0.4 and 0.56?    

Solution

Ans:

Given X be the pulling force as a multiple of its weight. Then X ~ N(0.4, 0.033)

Find p(X>0.4)=?

Converting into Z scores, we have, Z=0.4-0.4/0.033=0

P(Z>0)= 0.5 (from the Z tables)

Thus, p(X>0.4)= p(Z>0)= 0.5

Find p(0.4<X<0.56)=?

Converting into Z scores, z1= 0.4-0.4/0.033= 0

And z2= 0.56-0.4/0.033= 4.8484

Thus, p(0<z<4.8484)= 0.5 from the tables because the maximum value taken by Z values is around 3.