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iren [92.7K]
3 years ago
8

A machine produces defective parts with three different probabilities depending on its state of repair. If the machine is in goo

d working order, it produces defective parts with probability 0.02. If it is wearing down, it produces defective parts with probaly 0.1. If it needs maintenance, it produces defective parts with probability 0.3. The probability that the machine is in good working order is 0.8; the probability that it is wearing down is 0.1; and the probability that it needs maintenance is 0.1
(a) Given a good working machine, compute the probability that one of its randomly selected parts will be defective.
(b) Compute the probability that a randomly selected part will be defective.
(c) Suppose a randomly selected part is not defective. Compute the probability that it comes from a machine that needs maintenance.
Mathematics
1 answer:
Zina [86]3 years ago
6 0

Answer:

Step-by-step explanation:

Given that a machine produces defective parts with three different probabilities depending on its state of repair.

condition             Good order         Wearing down               Needs main   Total

Prob                       0.8                            0.1                                   0.1              1

Defective               0.02                          0.1                                   0.3

Joint prob              0.016                         0.01                                0.03        0.056

a) 0.016

b) total = 0.056

c) If not defective from needs maintenance

Prob for not defective = 0.8*0.98+0.1*0.9+0.1*0.7\\=0.784+0.09+0.07\\=0.944

From machine that needs maintenance = 0.07

So reqd prob = \frac{0.07}{0.944} \\=0.0741

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Brady made a scale drawing of a rectangular swimming pool on a coordinate grid. The points (-20, 25), (30, 25), (30, -10) and (-
djverab [1.8K]

Answer:

Length = 50 units

width = 35 units

Step-by-step explanation:

Let A, B, C and D be the corner of the pools.

Given:

The points of the corners are.

A(x_{1}, y_{1}})=(-20, 25)

B(x_{2}, y_{2}})=(30, 25)

C(x_{3}, y_{3}})=(30, -10)

D(x_{4}, y_{4}})=(-20, -10)

We need to find the dimension of the pools.

Solution:

Using distance formula of the two points.

d(A,B)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}----------(1)

For point AB

Substitute points A(30, 25) and B(30, 25) in above equation.

AB=\sqrt{(30-(-20))^{2}+(25-25)^{2}}

AB=\sqrt{(30+20)^{2}}

AB=\sqrt{(50)^{2}

AB = 50 units

Similarly for point BC

Substitute points B(-20, 25) and C(30, -10) in equation 1.

d(B,C)=\sqrt{(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}}

BC=\sqrt{(30-30)^{2}+((-10)-25)^{2}}

BC=\sqrt{(-35)^{2}}

BC = 35 units

Similarly for point DC

Substitute points D(-20, -10) and C(30, -10) in equation 1.

d(D,C)=\sqrt{(x_{3}-x_{4})^{2}+(y_{3}-y_{4})^{2}}

DC=\sqrt{(30-(-20))^{2}+(-10-(-10))^{2}}

DC=\sqrt{(30+20)^{2}}

DC=\sqrt{(50)^{2}}

DC = 50 units

Similarly for segment AD

Substitute points A(-20, 25) and D(-20, -10) in equation 1.

d(A,D)=\sqrt{(x_{4}-x_{1})^{2}+(y_{4}-y_{1})^{2}}

AD=\sqrt{(-20-(-20))^{2}+(-10-25)^{2}}

AD=\sqrt{(-20+20)^{2}+(-35)^{2}}

AD=\sqrt{(-35)^{2}}

AD = 35 units

Therefore, the dimension of the rectangular swimming pool are.

Length = 50 units

width = 35 units

7 0
3 years ago
A woman is randomly selected from the 18-24 age group. For women of this group, systolic blood pressures (in mm Hg) are normally
dybincka [34]

Answer:

0.0274

Step-by-step explanation:

The mean is \mu =114.8 and the standard deviation is \sigma =13.1.

Calculate

Z=\dfrac{X-\mu}{\sigma}

for X=140:

Z=\dfrac{140-114.8}{13.1}\approx 1.9237.

If X\sim N(114.8,\ 13.1), then Z\sim N(0,1)

and

Pr(X>140)=Pr(Z>1.9237).

Use table for normal distribution probabilities to get that

Pr(Z>1.9237)=1-Pr(Z\le 1.9237)=1-0.9726=0.0274.

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Answer:

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Step-by-step explanation:

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Answer:

180 I think

Step-by-step explanation:

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The dimension would be 10, i think


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