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andrezito [222]
3 years ago
11

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the en

tire batch is accepted if every item in the sample is okay. The ABC Electronics Company has just manufactured 1950 write-rewrite CDs, and 120 are defective. If 4 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?
Mathematics
1 answer:
zysi [14]3 years ago
4 0

Answer:

0.7755

Step-by-step explanation:

If 120 CDs are defective, the number of non-defective CDs in the batch is:

n=1950-120\\n=1830

In order for the batch to be accepted, all of the 4 CDs in the sample must not be defective, the probability of that happening is:

P=\frac{1830}{1950}*\frac{1829}{1949} *\frac{1828}{1948} *\frac{1827}{1947}\\P=0.7755

The probability that the entire batch will be accepted is 0.7755.

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A cashier has a total of 30 bills consisting of ones, fives and twenties. the number of twenties is 5 less than the number of on
Varvara68 [4.7K]

Let us say that:

a = ones

b = fives

c = twenties

 

So that the total money is:

1 * a + 5 * b + 20 * c = 229

=> a + 5b + 20c = 229                                       --> eqtn 1

 

We are also given that:

c = a – 5                                                                --> eqtn 2

a + b + c = 30                                                      --> eqtn 3

 

Rewriting eqtn 3 in terms of b:

b = 30 – a – c

Plugging in eqtn 2 into this:

b = 30 – a – (a – 5)

b = 35 – 2a                                                           --> eqtn 4

 

Plugging in eqtn 2 and 4 into eqtn 1:

a + 5(35 – 2a) + 20(a – 5) = 229

a + 175 – 10a + 20a – 100 = 229

11a = 154

a = 14

 

So,

b = 35 – 2a = 7

c = a – 5 = 9

 

Therefore there are 14 ones, 7 fives, and 9 twenties.

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3 years ago
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Agata [3.3K]

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3 0
3 years ago
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Answer:

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Step-by-step explanation:

Expressing the ratios as fractions, that is

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Given

\frac{2a+3b}{4b+3c} , substitute values from above for a and c

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