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The Book does not show any answers. Hence I need to figure out if I have done them correctly or not. Please help me if you can. Would greatly appropriate it. Thanks
A factory produced 4 preliminary shipments. The first shipment produced 360 units and each subsequent shipment produced twice as many units as the previous shipment. If the first shipment produced 2 defective units, the second and third shipment each produced 4 defective units, and fourth shipment produced 8 defective units, how many defective units can the factory expect from a shipment of 9,000 units based on the ratio of defective units to non-defective units from these preliminary shipments?
A. 20
B. 30
C. 40
D. 127.5
E. 270
A factory produced 4 preliminary shipments. The first shipment produced 360 units and each subsequent shipment produced twice as many units as the previous shipment. If the first shipment produced 2 defective units, the second and third shipment each produced 4 defective units, and fourth shipment produced 8 defective units, how many defective units can the factory expect from a shipment of 9,000 units based on the ratio of defective units to non-defective units from these preliminary shipments?
A. 20
B. 30
C. 40
D. 127.5
E. 270
phoenix9801
Total units produced is 360 + 360*2 + 360*4 + 360*8 = 360(1 + 2 + 4 + 8) = 360*15 = 5,400.
Total defective units is 2 + 4 + 4 + 8 = 18.
The ratio of defective units to non-defective units is 18/5,400 = 1/300 (1 defective unit out of 300).
So, based on this statistics the factory should expect 9,000*1/300 = 30 defective units from a shipment of 9,000 units.
Answer: B.
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PareshGmat
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Posts: 1,531
I did not multiplied or added
======================
I shipment = 360
IInd = 360x2
IIIrd = 360 x 4
IVth = 360 x 8
Total = 360 x (8+4+2+1) = 360 x 15 ----------------------
Defectives for above = 8 + 4 + 4+ 2 = 18; so for 9000 is :
9000 x 18 / (360 x 15) = 30
======================
I shipment = 360
IInd = 360x2
IIIrd = 360 x 4
IVth = 360 x 8
Total = 360 x (8+4+2+1) = 360 x 15 ----------------------
Defectives for above = 8 + 4 + 4+ 2 = 18; so for 9000 is :
9000 x 18 / (360 x 15) = 30
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