7. Ford Motor Company procures a part from two suppliers. The length of this par

Question

7. Ford Motor Company procures a part from two suppliers. The length of this part when producs supplier A is normally distributed with a mean of 1ocm and standard deviation of 2cm. At the are normally distributed with a mean of 10cm and sta time, the length of supplier B's parts deviation of 2.5cm. a. (3 pts) If consistency is an important factor for Ford, which supplier should be preferred Explain b. (7 pts) If a Ford engineer randomly selects one part from supplier A's shipment and one y supplier B's shipment, what is the probability that the part from supplier A is longer part from supplier B by at least 0.5cm? Cauim dintribution het ween 0 and 2.1

Explanation / Answer

A) Consider the randov variable

X: the length of the part produced by supplier A.

X ~ N( mean= 10 ,variance=4)

Y: the length of the part produced by supplier B.

Y ~ N( mean= 1, variance=6.25)

Coefficient of variation (A) = (S.D.(X) /abs(X bar))*100%

=( 2/10)*100%= 20%

Coefficient of variation (B) = (S.D.(Y) /abs(Y bar))*100%

=( 2.5/10)*100%= 25%

Since C.V(A)< C.V.(B).

The length of the part produced by suppiler A is more consistent.

The Supplier A should be preferred.

B) X-Y~ N( 0, 10.25)

Required probabilty = P(X-Y>0.5)

= P( (x-y)-0/3.2015)>(0.5-0)/3.2015)

=P(Z> 0.1561) Where Z ~ N(0,1)

From normal probability table

P(Z> 0.1561) = 0.438

P(X-Y>0.5) = 0.438

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