In: Statistics and Probability
A specialized machine manufacturer needs to purchase rivets whose strength is greater than 10,000 psi. There are two possible suppliers. Supplier A produces rivets with an average resistance of 14,000 psi with a standard deviation of 2000 psi. Supplier B produces the rivets with an average resistance of 13,000 psi and a standard deviation of 1500 psi. Both populations are normally distributed.
a. Which manufacturer will produce the smallest proportion of “faulty” rivets?
Assume that you decide to buy from manufacturer B:
b. What will be the expected number of defective rivets in a batch of 1000 units?
c. How many rivets on average will have to be tried to find a faulty one?
d. If it is desired that the proportion of defectives does not exceed 1%, where should the average be placed?
ANSWER:
a)
For Supplier A:
µ = 14000
σ = 2000
P( X ≤ 10000 ) = P( (X-µ)/σ ≤
(10000-14000) /2000)
=P(Z ≤ -2.00 ) = 0.02275
For Supplier B:
µ = 13000
σ = 1500
P( X ≤ 10000 ) = P( (X-µ)/σ ≤
(10000-13000) /1500)
=P(Z ≤ -2.00 )
= 0.02275
Both are same
b)
Mean = np
=1000*0.0228
= 22.75
c)
Number need to be tried = 1/ 0.02275
= 43.95578902
=46
d)
µ = 13490
σ = 1500
P( X ≤ 10000 ) = P( (X-µ)/σ ≤
(10000-13490) /1500)
=P(Z ≤ -2.33 ) = 0.00999
Average = 13490
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