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Vikki [24]
3 years ago
9

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 2100 write-rewrite CDs, and 60 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted
Mathematics
1 answer:
mrs_skeptik [129]3 years ago
5 0

Answer:

0.9167 = 91.67% probability that the entire batch will be accepted

Step-by-step explanation:

The CDs are chosen without replacement, which means that the hypergeometric distribution is used.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

2100 write-rewrite CDs, and 60 are defective.

This means, respectively, that N = 2100, k = 60

3 of these CDs are randomly selected for testing

This means that n = 3

What is the probability that the entire batch will be accepted?

Probability of none defective, so P(X = 0).

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 0) = h(0,2100,3,60) = \frac{C_{60,0}*C_{2040,3}}{C_{2100,3}} = 0.9167

0.9167 = 91.67% probability that the entire batch will be accepted

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noname [10]
Like XZ divides the cord YV into two congruent parts (YW=5.27 cm=WV), this segment XZ must be perpendicular to the segment YV, then the angle XWY in triangle XWY is a right angle (90°) and the triangle XWY is a right angle.

We can apply the trigonometric ratios in triangle XWY:
Hypotenure: XY
sin 44°=(Opposite leg to 44°)/(hypothenuse)
sin 44°=YW/XY
sin 44°=(5.27 cm)/XY
Solving for XY. Cross multiplication:
sin44° XY=5.27 cm
Dividing both sides of the equation by sin 44°:
sin 44° XY / sin 44° = (5.27 cm)/sin 44°
XY=(5.27/sin 44°) cm
XY=(5.27/0.694658370) cm
XY=7.586462929 cm

This value XY is the radius of the circle, then:
XZ=XY→XZ=7.586462969 cm

tan 44°=(Opposite leg to 44°) / (Adjacent leg to 44°)
tan 44°=YW/XW
tan 44°=(5.27 cm)/XW
Solving for XW. Cross multiplication:
tan 44° XW=5.27 cm
Dividing both sides of the equation by tan 44°:
tan 44° XW / tan 44°=(5.27 cm)/tan 44°
XW=(5.27/tan 44°) cm
XW=(5.27/0.965688775) cm
XW=5.457244753 cm

WZ=XZ-XW
WZ=7.586462969 cm-5.457244753 cm
WZ=2.129218216 cm
Rounded to 2 decimal places:
WZ=2.13 cm

Answer: The <span>measurement is closest to the measure of segment WZ is
2.13 cm</span>
6 0
3 years ago
Anyone wanna help me out
Sholpan [36]

Answer:

58.91m^2

Step-by-step explanation:

(smaller triangle below)

A=\frac{ab}{2}\\ =\frac{8.6*5.5}{2}\\ =23.65m^2\\\\A=\frac{ab}{2}\\ =\frac{8.6*8.2}{2} \\=35.26m^2

(bigger triangle above)

Since you have both triangle, and all lengths you dont need to worry about calculating the square

Add both together

23.65+35.26\\=58.91m^2

5 0
3 years ago
Read 2 more answers
2x+3=9 what is the answer
xxMikexx [17]

Answer : x=3

Step-by-step explanation:

Explanation:

2x+3=9

We want to find the variable x, so we have to make it alone. To do so, first subtract 3 from both sides of the equation:

2x+3  −  3=9  −  3

2x=6

Now divide both sides by 2:

2x2=62

So the final answer is:

x=3

6 0
3 years ago
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bija089 [108]
8. 6m + 3n
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3 years ago
Cassandra's Cogs advertises on its website that 90% of customer orders are received within three working days. They performed an
nikklg [1K]

Answer:

Part A: yes

Part B: 50%

Step-by-step explanation:

There are two ways we can use a normal approximation for a sample: if the population it is from is normally distributed, or if the sample is sufficiently large (n > 30).  In this case, we don't know if the population is normally distributed, but we do know the sample size is larger than 30, so we can use normal approximation.

The sample proportion is normally distributed, with a mean equal to the mean of the population.  So there is a 50% chance that sample proportion is less than the population proportion.

3 0
3 years ago
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