1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
strojnjashka [21]
3 years ago
13

Inclusions are defects in poured metal caused by contamitants. The number of (large) inclusions in cast iron follows a Poisson d

istribution with a mean of 2 per cubic millimeter. Deter mine the following:
a. Probability of at least one inclusion in a cubic millimeter.
b. Probability of at least 3 inclusions in 4.0 cubic millimeters.
c. Volume of material to inspect such that the probability of at least one inclusion is 0.98
d. Determine the mean inclusion per cubic millimeter such that the probability of at least one inclusion is 0.98.
Mathematics
1 answer:
GarryVolchara [31]3 years ago
8 0

Answer and Step-by-step explanation:

Solution: given:

(a)

Mean = λ = µ = 2permm3

By using formula:

P(x = k) =  λk e- λ  / k!

P ( not A) = 1 – p(A)

Passion probability at k = 0

P( x = 0) = 20 e-2/ 0!

               = 0.1353

Probability of at least one inclusion:

P(x≥1) = 1- p(x=0) = 1 – 0.1353

            = 0.864

(b) Probability of at least 3 inclusions in 4.0 cubic millimeters.

Mean = λ = µ = 2 per mm3

Inclusion in 4 cubic mm = 4 x 2 per 4 mm3 = 8 per 4 mm3

P(not A) = 1 – p(A)

Passion probability at k = 0,1,2

P(x=0) = 80 e-8 / 0!

        = 0.00034

P(x = 1) = 81 e-8 / 1!

            = 0.00272

P(x = 2) = 82 e-8 / 2!

              = 0.01088

Probability at least 3 inclusion:

P(x≥3) = 1 – p(x<3) = 1 – p(x = 0) – p(x =1) – p(x = 2)

            = 1 – 0.00034 – 0.00272 – 0.01088

          = 0.98606

(c) . Volume of material to inspect such that the probability of at least one inclusion is 0.98

The probability of x ≥ 1 has to be equal to 0.98

P(x ≥ 1) = 0.98

P(x = 0) = p(x < 1)

            = 1 – p(x≥ 1) = 1 – 0.98

            = 0.02

Poission probability at k = 0

P(x = 0) = (2 n )0 e-2n / 0! = e-2n

e-2n = 0.02

taking ln on both sides :

-2 n = ln e-2n = ln 0.02

Divided by -2,

n = ln 0.02 / -2

    = 1.955

Volume is 1.955 mm3.

(d) Determine the mean inclusion per cubic millimeter such that the probability of at least one inclusion is 0.98.

The probability of x ≥ 1has to be at least 0.98

P(x ≥ 1 )≥ 0.98

P(x = 0 ) = p(x < 1 ) = 1 – p(x≥1) =  1- 0.98

           = 0.02

Poisson probability at k = 0

P(x = 0) = λ0 e-λ / 0! = e-λ

e-λ ≤ 0.02

taking ln on both sides:

ln e-λ ≤ ln 0.02

λ = ln 0.02 / -1

    = 3.912

You might be interested in
The table below shows the cost for different numbers of tickets.
Black_prince [1.1K]

Answer:

D

Step-by-step explanation: It's not going up by 6 or 2, and it's not going down in numbers, so D

7 0
3 years ago
What's the standard form of 314,207
maria [59]
Standard form: 314,207

expanded form: 300,000+10,000+200+7

word form: three hundred fourteen thousand, two hundred seven

6 0
3 years ago
Which equation is true when x = 5? A 8x = 80 B x + 4 = 9 C 10 ÷ x = 5 D x − 6= 1
Pie

Answer:

B

Step-by-step explanation:

A. 8 * x = 80

8 * 5 = 40. 40 is not 80, so it doesn't work.

B. x + 4 = 9

5 + 4 = 9. This works.

C. 10 ÷ x = 5

10 ÷ 5 = 2. 5 is not 2, so it doesn't work.

D. x - 6 = 1

5 - 6 = -1. 1 is not -1, so it doesn't work.

5 0
2 years ago
Write a positive or negative integer that represents the situation. You earn $15 raking leaves. The integer represents the situa
beks73 [17]

Answer:

+$15

Step-by-step explanation:

Amount earned for raking leaves = $15

Representing the amount earned above. As a positive or negative integer will depend on what the money is used for or stands for.

Amount earned for working adds to one's wealth while expenses will be represented as negative as it decreases the amout one has ;

Hence, integer ; +$15

8 0
3 years ago
An airplane is traveling at a speed of 240 miles/hour with a bearing of 110°. The wind velocity is 56 miles/hour at a bearing of
vodka [1.7K]

Answer:

Actual speed = 288 miles per hour

Actual direction angle = 116.38^\circ

Step-by-step explanation:

"Bearing" is the relative position of an object outside the plane compared to the position of the plane.  

Heading the the direction the nose of the plane is pointing.  

Course is the direction that pilot wants the plane to go.  

Wind direction is always the direction the wind is blowing from.  

The airplane is traveling at a speed of 240 miles/hour with a bearing of 110°.  

If the plane is traveling with a bearing of 110° and the wind is blown at a bearing of 325°.  

 325^{\circ}- 110^{\circ} =225^{\circ}

215^{\circ}- 180^{\circ} =35^{\circ}

The Ground speed will be in excess of the airspeed and true direction will be south if the indicated heading.  

The tailwind component is:

56 cos (35^\circ)

And the cross wind component is:

56 sin (35^\circ)  


And that is,

C^2 = (286)^2 + (32)^2


c = 288

So the actual speed of the plane is 288 miles per hour.

The deviation in the direction is:

Let the direction angle be 'x'.

x = tan ^{-1}\left ( \frac{32}{286} \right )=6.38^\circ

So the actual direction angle is 110^\circ+ 6.38^\circ=116.38^\circ.

5 0
3 years ago
Other questions:
  • How do you reduce the number 6 33/16
    10·2 answers
  • Suppose that F(x) = x2 and G(x) = 2x2 – 5. Which statement best compares
    13·2 answers
  • Evaluate the expression described below if the number is –3.
    14·2 answers
  • How do you do two step equations: integers
    15·1 answer
  • 4<br> What is the value of the expression (81 1/4)4<br> ?
    14·1 answer
  • F(x) x2+5x-4<br>rewrite each equation in vertex form
    6·2 answers
  • A corner store sells two kinds of baked goods: cakes and pies. A cake costs $5 and a pie costs $7. In one day, the store sold 15
    13·1 answer
  • Which ratio is proportional to 10/24<br><br> A 20/36<br> B 5/8<br> C 35/84<br> D 5/6
    15·1 answer
  • Triangle GHJ with vertices G(-2, 4), H(3, 6), and J(3, -2) is dilated by a factor of 1/3 centered at the origin. What are the co
    11·1 answer
  • Which of these numbers: 3,4,18,111,123,340,345,456,555 are divisible by 3 but not 9
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!