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
zysi [14]
3 years ago
14

A certain kind of sheet metal has, on average, 3 defects per 18 square feet. Assuming a Poisson distribution, find the probabili

ty that a 31 square foot metal sheet has at least 4 defects. Round your answer to three decimal places.
Mathematics
1 answer:
Fofino [41]3 years ago
8 0

Answer:

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

In this problem, we have that:

3 defects per 18 square feet.

So for 31 square feet, we have to solve a rule of three

3 defects - 18 square feet

x defects - 31 square feet

18x = 3*31

x = \frac{31*3}{18}

x = 5.17

So \mu = 5.17

Assuming a Poisson distribution, find the probability that a 31 square foot metal sheet has at least 4 defects.

Either it has three or less defects, or it has at least 4 defects. The sum of the probabilities of these events is decimal 1.

So

P(X \leq 3) + P(X \geq 4) = 1

We want P(X \geq 4)

So

P(X \geq 4) = 1 - P(X \leq 3)

In which

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-5.17}*(5.17)^{0}}{(0)!} = 0.0057

P(X = 1) = \frac{e^{-5.17}*(5.17)^{1}}{(1)!} = 0.0294

P(X = 2) = \frac{e^{-5.17}*(5.17)^{2}}{(2)!} = 0.0760

P(X = 3) = \frac{e^{-5.17}*(5.17)^{3}}{(3)!} = 0.1309

So

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0057 + 0.0294 + 0.0760 + 0.1309 = 0.242

Finally

P(X \geq 4) = 1 - P(X \leq 3) = 1 - 0.242 = 0.758

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

You might be interested in
Which equation is modeled below? 3 long x tiles and 2 negative 1 tiles = 2 long x tiles and 4 square 1 tiles Negative 2 x + 3 =
balu736 [363]

Answer

The answer is D. 3x+(-2)=2x+4

5 0
2 years ago
Read 2 more answers
3.5.2 Test (CSI) Question 6 of 12 Use the area of the rectangle to find the area of the triangle. 5 ft 10 ft O A. The area of th
Jlenok [28]

Answer:

c

Step-by-step explanation:

3 0
3 years ago
How do you get this answer ?
Leno4ka [110]
If you 
Let x to be the total number of pages in a book,

then 1/3x = 117

because 117 = 1/3 of a book
5 0
3 years ago
How many degrees does a minute hand of a clock turn through from 6:20 am to8:00 am on the same day ? A. 680 degrees B. 600 degre
Phoenix [80]

Answer:

B 600

Step-by-step explanation:

A clock is a circle with 12 equal sectors. A circle has 360 degrees so every time a minute hand number goes to another number it changes 30 degrees. After a full hour the time is 7 20 and it changes 360 degrees since the minute hand change over time was 12. 30x12=360.

Then it from 7 :20 and 8 00 the change 8 so is 30×8=240

360+240=600

3 0
3 years ago
Are both students earning the same amount of money per hour? Show your work to justify your answer.
krok68 [10]

Answer:

No, Jimmy is earning $5 per hour while Amanda is earning close to $6.66 per hour.

Step-by-step explanation:

Have a nice day/night :)

7 0
2 years ago
Read 2 more answers
Other questions:
  • What’s the answer? Please help me
    10·1 answer
  • The data below shows the temperature of the water in a swimming pool over a two week period.
    13·1 answer
  • Help please :) ! The dashed triangle is the image of the pre-image solid triangle. What is the scale factor used to create the d
    9·2 answers
  • alexas bought 1 gallon of milk she had a recipe that calls for one quart of milk after making the recipe, how many quarts of mil
    15·2 answers
  • A video game cost $34.90 plus 10% tax. How much will you pay in all for the game?
    5·2 answers
  • Estimate a 15% tip on a dinner bill of $31.22 by first rounding the bill amount to the nearest ten dollars
    12·2 answers
  • 2 x (7-4)^2 - (8 x 2 + 2)/2 = <br><br> (the x indicates multiply)
    9·1 answer
  • Eric Tangler prism with the value of 10 cubic units is filled with cubes the side lengths of 1/2 unit how many 1/2 unit cubes do
    15·1 answer
  • Find the area of the shaded region. geometry please help if your good at it. will mark brainlist
    15·1 answer
  • Help pls Ill mark brainliest
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!