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A computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts S1,S2,S3 and S4 comined as shown in the table above. What is the expected number of defective chips in a shipment of 60000 chips?

Re: PS from OG 11th [#permalink]
19 Mar 2006, 07:09

1

This post received KUDOS

foolbox wrote:

shipment, # of defective chips, total # of chips S1 2 5,000 S2 5 12,000 S3 6 18,000 S4 4 16,000

A computer chip manufacturer expects the ratio of the # of defective chips to the total # of chips in all future shipments to equal the corresponding ratio for shipments S1,S2,S3, and S4 combined, as shown in the table above. What is the expected number of defective chips in a shipment of 60,000 chips?

Say X is the number of defective ships in the shipment of 60,000

we can write out the following equation

2+5+6+4/5,000+12,000+18,000+16,000 = X/60,000

17/51,000 = X/60,000

51,000X= 1,020,000
X= 20 _________________

The greater the sacrifice, the greater the Victory

Re: PS from OG 11th [#permalink]
19 Mar 2006, 08:38

foolbox wrote:

shipment, # of defective chips, total # of chips S1 2 5,000 S2 5 12,000 S3 6 18,000 S4 4 16,000

A computer chip manufacturer expects the ratio of the # of defective chips to the total # of chips in all future shipments to equal the corresponding ratio for shipments S1,S2,S3, and S4 combined, as shown in the table above. What is the expected number of defective chips in a shipment of 60,000 chips?

How come we can't solve this problem like;

Viewing package S1, and using proportional

2:5,000 = X:60,000

X = 60,000 * 2 / 5,000 = 24

Doesn't that make sense, guys?

pls, correct my misunderstading... _________________

Re: PS from OG 11th [#permalink]
19 Mar 2006, 08:44

foolbox wrote:

foolbox wrote:

shipment, # of defective chips, total # of chips S1 2 5,000 S2 5 12,000 S3 6 18,000 S4 4 16,000

A computer chip manufacturer expects the ratio of the # of defective chips to the total # of chips in all future shipments to equal the corresponding ratio for shipments S1,S2,S3, and S4 combined, as shown in the table above. What is the expected number of defective chips in a shipment of 60,000 chips?

How come we can't solve this problem like;

Viewing package S1, and using proportional

2:5,000 = X:60,000

X = 60,000 * 2 / 5,000 = 24

Doesn't that make sense, guys?

pls, correct my misunderstading...

We can't just take one shipment and make and equation since the stem explicitly states .." in all future shipments to equal the corresponding ratio for shipments S1,S2,S3, and S4 combined".

So you must have all the values in the equation _________________

The greater the sacrifice, the greater the Victory

Re: PS from OG 11th [#permalink]
20 Mar 2008, 07:59

foolbox wrote:

shipment, # of defective chips, total # of chips S1 2 5,000 S2 5 12,000 S3 6 18,000 S4 4 16,000

A computer chip manufacturer expects the ratio of the # of defective chips to the total # of chips in all future shipments to equal the corresponding ratio for shipments S1,S2,S3, and S4 combined, as shown in the table above. What is the expected number of defective chips in a shipment of 60,000 chips?

The key phrase in this question is "expects the ratio of the # of defective chips to the total # of chips in all future shipments to equal the corresponding ratio for shipments S1,S2,S3, and S4 combined".

To rephrase the sentense, if there are 17 defects to 51,000 chips, what is the proportion of defect for 60,000 chips? => 60,000 / 51,000 * 17 = ~ 20 (19.9999) _________________

Re: Weighted Average [#permalink]
25 Oct 2010, 07:04

3

This post received KUDOS

Summing all the defective chips in the table gives you 2 + 5 + 6 + 4 = 17. Summing all the total number of chips in each shipment gives you 5k + 12k + 18k + 16k = 51k.

Then, setting up a ratio can help you solve the problem. Since you know there's 17 defective chips in a shipment of 51k, set that equal to x/60k and solve.

17/51k = x/60k 17/51k = 1/3k 1/3k = x/60k 60k/3k = x x = 20

Re: Weighted Average [#permalink]
30 Oct 2010, 00:23

I agree with your solution = 20. But the question is:

There are different combination to get 60,000 chips. For example: 1*S3 + 2*S4 + 2*S2. In this way, we ship 60,000 chips with only 6 + 4*2 + 2*2 = 18 defective chips, better than the average of 20.

The question is to find the expected number of defective chips, i guess it assume the minimum #, therefore it might not be 20.

Re: Practice Test 2 Q1 [#permalink]
31 Dec 2010, 19:10

There are (2+5+6+4 = 17) defective pieces in shipment of (5000+12000+18000+16000=51000) pieces. That is equivalent to 1 defective piece/3000 shipment of pieces.

So, in a shipment of 60000 pieces, there will be (1/3000) * 60000 = 20 defective pieces.

Re: A computer chip manufacturer [#permalink]
05 May 2012, 07:46

This question is total bullocks. Everyone here took a simple arithmetic average (Total number of Defective)/(Total number of all shipments). I took a weighted average. Obviously the larger shipments should get more weight. Does anyone agree the wording of this question is awkward?

Re: A computer chip manufacturer [#permalink]
06 May 2012, 01:48

Expert's post

alphabeta1234 wrote:

This question is total bullocks. Everyone here took a simple arithmetic average (Total number of Defective)/(Total number of all shipments). I took a weighted average. Obviously the larger shipments should get more weight. Does anyone agree the wording of this question is awkward?

There is nothing wrong with the question or the solutions.

A computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts S1,S2,S3 and S4 comined as shown in the table above. What is the expected number of defective chips in a shipment of 60000 chips? A. 14 B. 20 C. 22 D. 24 E. 25

Set up equation: \(\frac{x}{60,000}=\frac{2+5+6+4}{5,000+12,000+18,000+16,000}\) --> \(x=20\);

Or: \(2+5+6+4=17\) defective chips in \(5,000+12,000+18,000+16,000=51,000\) chips, so \(\frac{17}{51,000}=\frac{1}{3,000}\): 1 in 3,000. So, expected number of defective chips in a shipment of 60,000 chips is \(\frac{60,000}{3,000}=20\).

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