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

Answers

Answer 1

Answer:

a)  P(X>=1) = 0,7293        or   P(X>=1) =  72,93 %

b)  P(X>=3) = 0,5686     or     P(X>=3) = 56,86 %

c)  y =  0,8494 mm³

d) λ = 1,69897 inc per mm³

Step-by-step explanation:

a) P(X>=1) = 1 - P(X=0)

P(X = 0) = λ⁰ * e∧⁻λ / 0!          where λ  = 2 in/mm³

P(X = 0) = e∧-2    ⇒    P(X = 0) = 0,2706

Then

P(X>=1) = 1 - 0,2706

P(X>=1) = 0,7293        or   P(X>=1) =  72,93 %

b) 3 inc. in 4 mm³ = 2*4/3     λ = 2,67 inc. per mm³

P(X>=3)  =  1 - P(X=1 ) - P(X=2)

P(X=1) = λ¹ * e∧-λ / 1!    ⇒  P(X=1) = 2,67 *e∧- 2,67/1

P(X=1) = 0,1846

P(X=2) = λ² * e∧-λ / 2!   ⇒   P(X=2) = (2,67)² * e ∧ - 2,67/2

P(X=2) = 7,1289* 0,06925/2     ⇒  P(X=2) = 0,2468

Then

P(X>=3)  =  1 -  0,1846 - 0,2468

P(X>=3) = 0,5686     or     P(X>=3) = 56,86 %

c) P(X>=1) = 0,98

and λ = 2*y     where y is the quantity of material

P(X=0) = 1 -  P(X>=1)

P(X=0) = 1 - 0,98    P(X=0) = 0,02

0,02 = (2*y)⁰  * e ∧ -2*y /0!

0,02 = 1 *  e ∧ -2*y

Taking log on both sides of the equation

log (0,02) = -2*y        - 1,69897 = - 2*y

y =  0,8494 mm³

d) P(X  >=1 ) = 1 - P( X = 0)

0,98 = 1 - P( X = 0)

P( X = 0) = 0,02

0,02 = λ⁰ * e ∧ - λ / 0!

0,02 = e ∧ -λ

Taking log on both sides of the equation we get:

log ( 0,02 ) = - λ

- 1,69897  =  - λ

λ = 1,69897  inc. per mm³

 


Related Questions

Lara took a total of 10 pages of notes during 2 hours of class. After attending 9 hours of
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Fast please i need it asap thanks

Answers

Answer:

45 pages

Step-by-step explanation:

The unit rate is  the number of pages divided by the unit of time

10 pages /2 hours

5 pages per hour

To find the total number of pages of notes take, multiply the unit rate by the total amount of time

We have 9 hours

5 pages per hour * 9 hours

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Answer:

take x to be the no. of pages for 9 hours

10 pages                      2 hours

x pages                         9 hours

Cross multiplication:

90 = 2x

x = 90/2

x = 45

Lara will cmplte 45 pages in 9 hours.

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Answer:

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Uhdfburfuruhd

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Answers

Answer:

945

Step-by-step explanation:

Answer:

1730 (2 times the whole expression) or 945 (2 times the addend of 80) [what is implied when 80+ 185-40+699-59 is not in parenthesis]

Step-by-step explanation:

2 times (80 + 185 - 40 + 699 - 59) →

2 (80 + 185 - 40 + 699 - 59)

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2 ((265 - 40) + 699) - 59)

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2 (924 - 59)

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1730

_____________________

2 times 80 + 185 - 40 + 699 - 59 →

2(80) + 185 - 40 + 699 - 59

(((160 + 185) - 40) + 699) - 59

((345 - 40) + 699) - 59

(305 + 699) - 59

1004 - 59

945

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Step-by-step explanation:

if the mean of a negatively skewed distribution is 40 which of these values could be the median of the distribution
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Answers

Answer:

c.40

plz mark brainliest if helpful

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

He will need {3 POUNDS} to make 18 cups of chilli

Brainlist ??

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Answers

Answer:

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Answer:

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Step-by-step explanation: Hopefully that helps ;)

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Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Hope this helps! <3

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Answer:

The answer to this problem is 6.2

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Step-by-step explanation:

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Answers

simone is 15 years old.

Answer:

15 years old.

Step-by-step explanation:

Amanda is currently 25 years old.

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30/2=15.

Thus, Simone is 15 years old.

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Answer:

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Step-by-step explanation:

What is the probability that a randomly chosen male voter is a registered Democrat? Round your answer to the nearest tenth of a percent.

Answers

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Answers

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Step-by-step explanation:

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Answers

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Answers

Answer:

0.3

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 2.1

-1.8

---------

0.3

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30 POINTS BRAINLIEST

Annabelle lives at Bermondsey in London. She has to speak at a conference inBirmingham at 10.30am.

It will take her an hour from her home to get to Euston Rail
Station, from where she will get a train to Birmingham.

The train journey from Euston
to Bimingham is an hour and 10 minutes.

Trains to Birmingham run at the following times: 5 minutes past the hour, 25 minutes past the hour and 45 minutes past the hour.

The meeting venue in Birmingham is a 5-minute walk from the station.

What is the latest time that Annabelle can leave home, if she is to make it on time for
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Show your work.

Please HELP!!! DUE TODAY!!
Thank you so much.

Answers

Answer:

7:45

Step-by-step explanation:

work backwards from 10:30!

u need 5 min to walk from meeting place to station, therefore u need to done riding the train by 10:25.

then u know that the train is an hour and 30 min, therefore u have to ride the train before or at 8:55 (10:25 minus an hour and a half)

the latest time for the train to leave is 45 min past the hour. therefore you will ride the 8:45 train.

since we already know that we are riding the 8:45 train by latest, you have to leave an hour early to get to the station. so you need to leave home by 7:45.

hope i was helpful !

The latest time that Annabelle can leave home is the she leaves home and she won't be late for her meeting

Time of meeting = 10.30am

Time she will spend before getting to meeting:

home to get to Euston Rail Station = 1 hour

train journey from Euston to Bimingham = 1 hour 10 minutes

Trains to Birmingham = 5 minutes past the hour, 25 minutes past the hour and 45 minutes past the hour.

The latest time is 45 minutes

Walk from the meeting venue in Birmingham from the station = 5 minute walk

Total time = 1 hour + 1 hour 10 minutes + 45 minutes + 5 minutes

= 3 hours

Counting 3 hours backward from 10:30 am = 7:30 am

Therefore, the latest time Annabelle can leave home is 7:30 am

Read more:

https://brainly.com/question/3785992

what is the answer for this problem
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Answers

Answer:

9000

Step-by-step explanation:

10^3 means 10*10*10 which = 1000

1000*9 equals 9000

an easier way to think of this is just look at the exponet and add that many zeros to 9

Answer:

9,000

Step-by-step explanation:

9 X 10^3 = 9,000.

Hope it helps!

tolong bantu jawab please, makasih sebelumnya!

Answers

Answer:

2x² - 3x - 2

Explain:

Use the FOIL method: (a +b)(c +d) = ac + ad +bc +bd.

2x² + x - 4x - 2

Collect like terms.

2x² + (x - 4x) - 2

Simplify.

2x² - 3x - 2

21≥4x-15 solve
.....

Answers

Answer:

Inequality Form: x < 9

Interval Notation: (-∞,9)

I hope this helps

if you could, feel free to mark me Brainliest it would be much appreciated :D

If an area can be washed at a rate of 2,700 cm2/minute, how many square inches can be washed per hour? Enter your answer with the correct number of significant digits. Use the equivalent measures indicated. (1 centimeter ≈ 0.39 inch, 1 hour = 60 minutes)

Answers

Answer:

250,000

Step-by-step explanation:

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