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
Yuliya22 [10]
2 years ago
8

Suppose the following number of defects has been found in successive samples of size 100: 6, 7, 3, 9, 6, 9, 4, 14, 3, 5, 6, 9, 6

, 10, 9, 2, 8, 4, 8, 10, 10, 8, 7, 7, 7, 6, 14, 18, 13, 6.
a. Using all the data, compute trial control limits for a fraction-defective control chart, construct the chart, and plot the data.
b. Determine whether the process is in statistical control. If not, assume that assignable causes can be found and out of- control points eliminated.
Mathematics
1 answer:
Brut [27]2 years ago
7 0

Answer:

Given the data in the question;

Samples of size 100: 6, 7, 3, 9, 6, 9, 4, 14, 3, 5, 6, 9, 6, 10, 9, 2, 8, 4, 8, 10, 10, 8, 7, 7, 7, 6, 14, 18, 13, 6.

a)

For a p chart ( control chart for fraction nonconforming), the center line and upper and lower control limits are;

UCL = p" + 3√[ (p"(1-P")) / n ]

CL = p"

LCL = p" - 3√[ (p"(1-P")) / n ]

here, p" is the average fraction defective

Now, with the 30 samples of size 100

p" =  [∑(6, 7, 3, 9, 6, 9, 4, 14, 3, 5, 6, 9, 6, 10, 9, 2, 8, 4, 8, 10, 10, 8, 7, 7, 7, 6, 14, 18, 13, 6.)] / [ 30 × 100 ]

p" = 234 / 3000

p" = 0.078

so the trial control limits for the fraction-defective control chart are;

UCL = p" + 3√[ (p"(1-P")) / n ]

UCL = 0.078 + 3√[ (0.078(1-0.078)) / 100 ]

UCL = 0.078 + ( 3 × 0.026817 )

UCL = 0.078 + 0.080451

UCL = 0.1585

LCL = p" - 3√[ (p"(1-P")) / n ]

LCL = 0.078 - 3√[ (0.078(1-0.078)) / 100 ]

LCL = 0.078 - ( 3 × 0.026817 )

LCL = 0.078 - 0.080451

LCL =  0 ( SET TO ZERO )

Diagram of the Chart uploaded below

b)

from the p chart for a) below, sample 28 violated the first western electric rule,

summary report from Minitab;

TEST 1. One point more than 3.00 standard deviations from the center line.

Test failed at points: 28

Hence, we conclude that the process is out of statistical control

Lets Assume that assignable causes can be found to eliminate out of control points.

Since 28 is out of control, we should eliminate this sample and recalculate the trial control limits for the P chart.

so

p" = 0.0745

UCL = p" + 3√[ (p"(1-P")) / n ]

UCL = 0.0745 + 3√[ (0.0745(1-0.0745)) / 100 ]

UCL = 0.0745 + ( 3 × 0.026258 )

UCL = 0.0745 + 0.078774

UCL = 0.1532

LCL  = p" - 3√[ (p"(1-P")) / n ]

LCL = 0.0745 - 3√[ (0.0745(1-0.0745)) / 100 ]

LCL = 0.0745 - ( 3 × 0.026258 )

LCL = 0.0745 - 0.078774

UCL = 0  ( SET TO ZERO )

The second p chart diagram is upload below;

NOTE; the red circle symbol on 28 denotes that the point is not used in computing the control limits

You might be interested in
A robot that makes _/8 of a boat per day will make 7 boats in 8 days
Sidana [21]
7/8 boats per day will make it
8 0
3 years ago
5y-3y+1=7<br><br> solve for y
Juli2301 [7.4K]

Answer:

y=3

Step-by-step explanation:

Let's solve your equation step-by-step.

5y−3y+1=7

Step 1: Simplify both sides of the equation.

5y−3y+1=7

5y+−3y+1=7

(5y+−3y)+(1)=7(Combine Like Terms)

2y+1=7

2y+1=7

Step 2: Subtract 1 from both sides.

2y+1−1=7−1

2y=6

Step 3: Divide both sides by 2.

2y /2 = 6 /2

y=3

3 0
3 years ago
X^2 - 2x = 15 how do I solve this quadratic method?<br>I am stuck on it.... please help<br>​
Anarel [89]

Answer:

(x - 5)(x + 3)

Step-by-step explanation:

to solve x² - 2x = 15, we need to get all the terms on one side so we can solve the quadratic equation using factoring. to do this, we subtract 15 from both sides

x² - 2x = 15

- 15         -15

x² - 2x - 15 = 0

now we can factor. we need 2 numbers that when multiplied together give us -15, and when those 2 numbers are added together we get -2

because we have a -15, we can assume that one number must be negative and the other positive, as a negative times a postive is a negative.

we can use 3 and -5 as factors and test it out. we put x in front because we have an x²

(x - 5)(x + 3) < we can FOIL to check to see if this is correct. its not mandatory to check but when you arent sure of the answer you can FOIL it out

FOIL stands for: First, Outside, Inside, and Last terms

F: (x - 5)(x + 3) = x²

O: (x - 5)(x + 3) = -3x

I: (x - 5)(x + 3) = 5x

L: (x - 5)(x + 3) = -15

x² + 3x - 5x - 15 < subtract 3x from 5x

x² - 2x - 15

this checks out, so our answer is (x - 5)(x + 3)

6 0
2 years ago
Read 2 more answers
a deer tick measures 29 centimeters in length in a photograph. if the photo has been enlarged by a factor of 100, what is the ac
N76 [4]
.29 cm in length

29 ÷ 100 = .29
3 0
3 years ago
If x-3 is a factor of x3+4x2+kx-30.Find the value of k.​
Bogdan [553]

Answer:

k=-11

Step-by-step explanation:

x^{3}+4x^{2}+kx-30

if x-3 is a factor,

(3)^{3}+4(3)^{2}+k(3)-30=0\\27+4*9+3k-30=0\\27+36+3k-30=0\\33+3k=0\\3k=-33\\k=-11

3 0
3 years ago
Other questions:
  • Zelma buys p pounds of bananas for $0.40 per pound she pays the clerk with a $20 bill the clerk subtract the total cost of the b
    14·1 answer
  • Determine whether the improper integral converges or diverges, and find the value of each that converges.
    8·1 answer
  • Write a 2-column proof to prove the triangles congruent
    15·1 answer
  • How do you find the area of a compound figure?
    7·1 answer
  • WILL GIVE BRAINLIEST TO CORRECT ANSWER! HELP ASAP! I AM ON A TIME LIMIT! Classify the following triangle as acute, right or obtu
    10·2 answers
  • Which of the following ordered pairs could be placed in the table and still have the relation qualify as a linear function?
    15·2 answers
  • Express the following fraction in simplest form using only positive exponents.<br> 4(k)^4/3k9
    6·1 answer
  • The value of -4 5/8 - x is positive. What are two possible values of x?
    6·1 answer
  • Find each value if f(x) = 2x - 1 and g(x) = 2 - x2.
    10·1 answer
  • Solve the proportion for x
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!