Question

(S-AQ 3.57)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 µ = 0.37 and standard deviation s = 0.04

What proportion of adhesions (± 0.001) measured in use are higher than 0.36?  
What proportion of adhesions (± 0.001) are between 0.36 and 0.42?  

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	0.37
std deviation   =σ=	0.0400

1)

proportion of adhesions (± 0.001) measured in use are higher than 0.36 :

probability =

P(X>0.36)

=

P(Z>-0.25)=

1-P(Z<-0.25)=

1-0.4013=

0.599

2)

proportion of adhesions (± 0.001) are between 0.36 and 0.42 :

probability =

P(0.36<X<0.42)

=

P(-0.25<Z<1.25)=

0.8944-0.4013=

0.493