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Damm [24]
2 years ago
11

A shipment of 50 precision parts including 4 that are defective is sent to an assembly plant. The quality control division selec

ts 10 at random for testing and rejects the entire shipment if 1 or more are found defective. What is the probability this shipment passes inspection?
Mathematics
1 answer:
natali 33 [55]2 years ago
6 0

Answer:

0.3968 = 39.68% probability this shipment passes inspection.

Step-by-step explanation:

The parts are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes 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 successes.

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)!}

In this question:

50 parts means that N = 50

4 defective means that k = 4

10 are chosen, which means that n = 10

What is the probability this shipment passes inspection?

Probability that none is defective, so:

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

P(X = 0) = h(0,50,10,4) = \frac{C_{4,0}*C_{46,10}}{C_{50,10}} = 0.3968

0.3968 = 39.68% probability this shipment passes inspection.

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Please help asap!!!
sp2606 [1]

Answer:

y=\frac{1}{6} (x+5)^2-4.5

y=\frac{-1}{20} (x-10)^2+1

Step-by-step explanation:

focus at (-5, -3), and directrix y = -6

Directrix y=-6 so its  a vertical parabola

so equation is

(x-h)^2 = 4p(y-k)

(h,k) is the center

P is the distance between focus and vertex

distance between focus and directrix = 2p

distance between -3  and y=-6 is 3

2p = 3

p = 3/2 or p = 1.5

Focus is (h, k+p)

given focus is (-5, -3) so h= -5  and k+p = -3

k+p=-3, plug in 1.5 for p

k + 1.5 = -3

subtract 1.5 on both sides

k = -4.5

(x-h)^2 = 4p(y-k)

(x+5)^2= 4(1.5) (y+4.5)

(x+5)^2= 6(y+4.5)

divide by 6 on both sides

then subtract 4.5 on both sides

y=\frac{1}{6} (x+5)^2-4.5

focus at (10, -4), and directrix y = 6.

Directrix y=6 so its  a vertical parabola

so equation is

(x-h)^2 = 4p(y-k)

distance between focus and directrix = 2p

distance between -4  and y=6 is -4-6=-10

2p = -10

p = -5

Focus is (h, k+p)

given focus is (10, -4) so h= 10  and k+p = -4

k+p=-4, plug in 5 for p

k - 5 = -4

add 5 on both sides

k = 1

(x-h)^2 = 4p(y-k)

(x-10)^2= 4(-5) (y-1)

(x-10)^2= -20(y-1)

divide by -20 on both sides and add 1 on both sides

y=\frac{-1}{20} (x-10)^2+1


8 0
3 years ago
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