Answer to Question #234057 in Statistics and Probability for blossoms

Question

 A manufacturing company implemented a new production process to reduce defective fuses. From the old process, it was computed that at least 1 defect costs the company an average of ₱6,500,000.00 per production run. After implementing the new process, suppose a large lot contains 10% defective fuses and four fuses are randomly sampled from the lot. 

a.    Find the probability that at least one fuse in the sample of four is defective. 

b.    (Continuing from result in item a) in one production run of 500 eighty-unit lots, how much would be the loss if the cost to manufacture one unit is ₱ 335.75? 

c.     How much is the difference from the old process? Did the new process effectively reduce the company’s losses?

Answer 1

$a)\\ P(x≥1) = 1- P(x=0)= 1-(0.1*(1-0.1)^4)= 0.3439$

b)

Cost of manufacturing

$=335.75*500*80=13430000$

Loss $=10 \% * 1343000= 1343000$

c)

Difference from the old process

$=6500000-1343000=5157000$

Yes, the new process effectively reduces the company’s losses