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
Help! What si the verbal expression for this algebraic expression: 2x - 4 &lt; 4x +8
katrin2010 [14]

Answer:

C. Four less than the product of two and a number is less than the product of four and the same number increased by eight.

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Converting expressions to word form

Step-by-step explanation:

<u>Step 1: Define</u>

2x - 4 < 4x + 8

<u>Step 2: Translate</u>

"2x" is the product of two and a number <em>x</em>

" - 4" is four less

"<" is less than

"4x" is the product of four and a number <em>x</em>

" + 8" is increased by 8

<u>Step 3: Combine</u>

The difference between the product of two and a number <em>x</em> and 4 is less than the sum of the product of four and a number <em>x</em> and 8.

<u>Step 4: Reword</u>

Four less than the product of two and a number is less than the product of four and the same number increased by eight.

4 0
3 years ago
Read 2 more answers
The yearbook club is handing out T-shirts to its members. There are 5 blue, 7 green, 9 red, and 4 yellow T-shirts in all. If Jac
damaskus [11]

Answer:

n(R)=9

n(Y)=4

n(B)=5

n(G)=7

n(s)25

probability of getting red =n(R)/n(S)=9/25

6 0
3 years ago
Use a single digit times a power of 10 to express the number 866,214,000,000
BartSMP [9]

Answer:

8.66214 x 10^11

Step-by-step explanation:

question may ask to round, so the answer may be simplified to 9 x 10^11

3 0
3 years ago
What is the solution to this inequality?
Alika [10]

Answer:

<h2>A</h2>

Step-by-step explanation:

<em><u>e5uiitweyutwwsuoye34t</u></em>

3 0
3 years ago
Read 2 more answers
Find the product of x2 + 2x - 4 and 3x .
Mariulka [41]

Answer:x4+2x3+7x2+6x+12

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • What the sum to 4/9 + 3/18
    7·1 answer
  • Leslie is 3 times as old as her son. After 10 years, Leslie will be two times as old as her son, how old is Leslie and her son.
    15·2 answers
  • Amir and Edward are twins, They want to invite their friends to celebrate birthday party at a bowling alley. They have a budget
    5·1 answer
  • Can the statement be written as a biconditional statement and why?????
    13·1 answer
  • What is 3/4 to the power of 4 as a fraction?
    14·2 answers
  • 2n-5(n+5)=8n+3(1-5n) what does n equal to
    14·2 answers
  • I need help. (5+5)/2
    7·2 answers
  • Henri bought 3 jars of spaghetti sauce. He used a coupon that reduced the cost of each jar by $0.75. If he paid $6.72 altogether
    5·1 answer
  • Please help! Will give brainliest (10 points)
    12·2 answers
  • Use the spinner below to find each probability. Write as a fraction in simplest form.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!