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07 Aug 2024, 07:30
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (02:41) correct
40%
(02:27)
wrong
based on 73
sessions
History
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Not Attempted Yet
An assembly line produces car seats. 18% of the car seats produced by the factory are defective. 95% of the defective car seats were spotted during a routine quality check but 1% of the non-defective seats were also rejected by mistake. Approximately what percentage of the car seats cleared by the assembly line is defective?
(A) 1.1%
(B) 4.5%
(C) 5.7%
(D) 6.2%
(E) 10%
(A) 1.1%
(B) 4.5%
(C) 5.7%
(D) 6.2%
(E) 10%
08 Aug 2024, 03:14
Kudos
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The answer will be: (DEFECTIVE SEATS MISSED/TOTAL SEATS CLEARED)*100
Let the total car seats produced = \(100\)
Which means that 82 seats are not defective, and that 18 are.
1% of the non-defective seats were rejected by mistake: \(0.01*82 \) ≈ \(1\)
Which means that \(81\) of the non-defective seats were cleared.
5% of the defective seats were missed: \(0.05*18 \) ≈ \(1\)
Total seats cleared: \(81 + 1 = 82\)
Approximately what percentage of the car seats cleared by the assembly line is defective:\( \frac{1}{82}*100\) ≈ \(\frac{100}{80}\) ≈ \(1.25\)%
ANSWER A
Let the total car seats produced = \(100\)
Which means that 82 seats are not defective, and that 18 are.
1% of the non-defective seats were rejected by mistake: \(0.01*82 \) ≈ \(1\)
Which means that \(81\) of the non-defective seats were cleared.
5% of the defective seats were missed: \(0.05*18 \) ≈ \(1\)
Total seats cleared: \(81 + 1 = 82\)
Approximately what percentage of the car seats cleared by the assembly line is defective:\( \frac{1}{82}*100\) ≈ \(\frac{100}{80}\) ≈ \(1.25\)%
ANSWER A
08 Aug 2024, 17:01
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Bunuel
100x Total,
Total Defective = 18% = 18x
Non defective = 82x
Spotted Defective 95% means 5% are mistakenly there non defective carseats. \(= 0.05*18x = 0.9x\)
Plus, 1% of non defective mistakenly rejected \(= 1% of 82x = 0.82x \)
Total of actual non defectives \(= 82x-0.82x = 81.18x\)
Total of non defectives considering mistakenly selected defective \(= 81.18x + 0.9x = 82.08x\)
percentage of the car seats cleared by the assembly line is defective = \(\frac{0.9x}{82.08x} * 100 = 1.096%\)
Answer is A.
