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liubo4ka [24]
3 years ago
15

To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of

credits for the course. Suppose a student had these grades: 3.8 in a 5 credit Math course 1.8 in a 3 credit Music course 3.1 in a 5 credit Chemistry course 3.1 in a 5 credit Journalism course What is the student's GPA for that term? Round to two decimal places. Student's GPA =
Mathematics
1 answer:
postnew [5]3 years ago
4 0

Answer:

The student's GPA for that term is 3.07

Step-by-step explanation:

So this is a problem where we need to compute a weighted arithmetic mean.

To compute the weighted arithmetic mean of a set, we need to multiply each value of the set by their respective weight, add them, and then divide by the sum of the weights.

I will write the set in a {V,W} way, where V is the value(the grade) and W is the weight of V.

So your set G will be

G = {{3.8, 5}, {1.8,3}, {3.1,5}, {3.1,5}}.

Multiplying each value by it's respective weigth and then adding, we have:

3.8*5 + 1.8*3 + 3.1*5 + 3.1*5 = 19 + 5.4 + 15.5 + 15.5 = 55.4

The sum of the weigths is 5 + 3 + 5 + 5 = 18

So the student's GPA for that term, rounded to two decimal places, is: 55.4/18 = 3.07

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Step-by-step explanation:

remember, the number of possible combinations to pick m out of n elements is C(n, m) = n!/(m! × (n-m)!)

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so, the probability for one picked transistor to be defective is 1/25.

and the probability for it to work properly is then 1-1/25 = 24/25.

now, 500 picks are done.

to accept the shipment, 9 or less of these 500 picks must be defective.

the probability is then the sum of the probabilities to get

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1 defective = (24/25)⁴⁹⁹×1/25 × C(500, 1)

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2 defective = (24/25)⁴⁹⁸×1/25² × C(500, 2)

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3 defective = 24⁴⁹⁷/25⁵⁰⁰ × C(500, 3) =

= 24⁴⁹⁷/25⁵⁰⁰ × 250×499×166

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9 defective = 24⁴⁹¹/25⁵⁰⁰ × C(500, 9) =

= 24⁴⁹¹/25⁵⁰⁰ × 500×499×498×497×496×495×494×493×492×491 /

9×8×7×6×5×4×3×2 =

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best to use Excel or another form of spreadsheet to calculate all this and add it all up :

the probability that the engineer will accept the shipment is

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is the acceptance policy good ?

that completely depends on the circumstances.

what was the requirement about max. faulty rate in the first place ? if it was 2%, then the engineer's approach is basically sound.

it then further depends what are the costs resulting from a faulty unit ? that depends again on when the defect is usually found (still in manufacturing, or already out there at the customer site, or somewhere in between) and how critical the product containing such transistors is. e.g. recalls for products are extremely costly, while simply sorting the bad transistors out during the manufacturing process can be rather cheap. if there is a reliable and quick process to do so.

so, depending on repair, outage and even penalty costs it might be even advisable to have a harder limit during the sample test.

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