Suppose a quality control engineer wishes to estimate the proportion of defective items in a production line. i. (4 points) To estimate the proportion within 0.02 and with 98% confidence, what is the minimum required sample size if the company currently has no idea about the

Answers

Answer 1

Answer:

The minimum sample size required is 3385.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

To estimate the proportion within 0.02 and with 98% confidence, what is the minimum required sample size if the company currently has no idea about the

The minimum sample size required is n.

We find n when [tex]M = 0.02[/tex]

We don't know the true proportion, so we use [tex]\pi = 0.5[/tex], which is when the largest minimum sample size will be needed.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 2.327\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.02\sqrt{n} = 2.327*0.5[/tex]

[tex]\sqrt{n} = \frac{2.327*0.5}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.327*0.5}{0.02})^{2}[/tex]

[tex]n = 3384.33[/tex]

Rounding up

The minimum sample size required is 3385.


Related Questions

A tire salesman was paid a $25.90 commission after one of his customers purchased a set of new tires for $370. What is the commission rate?

Answers

Answer:

7%

Step-by-step explanation:

25.9÷370=0.07×100=7%

missy went to the store and bought 3 packs of candy. Each packs holds 5 chocolate bar. how many chocolate bars did missy but at the stores

Answers

Answer:

15

Step-by-step explanation:

5 x 3 = 15

Hope this helps ;)

Plane P cuts sphere o in a circle that has diameter
20. If the diameter of the sphere is 30, how far is the
plane from O?​

Answers

Answer:

  5√5 ≈ 11.18 units

Step-by-step explanation:

The Pythagorean theorem can be used to find the unknown leg of a triangle with hypotenuse 15 and one leg 10:

  d = √(15^2 -10^2) = 5√(3^2 -2^2) = 5√5

The plane is 5√5 units from the center of the sphere.

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In a baseball field, the arc that divides the outfield from the infield has a radius of 95 feet measured from the pitching rubber. The degree
measure of the arc is about 145. What is the length of the arc to the nearest foot?
A
481 ft
B. 13,775 ft
C. 180 ft
D. 240 ft
Back
Net
on
4

Answers

Answer:

240

Step-by-step explanation:

PLS HELP ME!
Um doing venn digrams so u have to set one up for it to work... TWENTY POINTS

Answers

Answer:

Creating a diagram..

Step-by-step explanation:

Alrighty, I've made a diagram. I've even uploaded it so everyone can see how good at drawing I am (not)

a. 7 do not own anything.

b. the probability that someone owns a bone or a stick is 50%.

c. the probability that someone owns a rock and a bone is 14%.

d. the probability that someone owns at least 2 items is 42%.

e. the probability that someone owns only 1 of these items is 51%.

Please tell me if im wrong! im only a student .m.

Barnes and Nobles buys a book for $14.25. They markup the price of the book by 35%.

Answers

Answer:

$19.24

Step-by-step explanation:

Take 14.25 times 1.35.

The markup rate will be 35% when the cost of the book is $14.25 and sells for $19.237.

What is the markup rate?

The markup rate is computed by dividing a unit's gross profit (its sales price less its cost to create or buy for resale) by its cost.

Barnes and Noble buy a book for $14.25. They mark up the price of the book by 35%.

As per the question, we have

cost = $14.25

markup rate = 35% = 0.35

Let's x represent markup for the book,

markup rate = markup/sale price × 100%

35% = x / $14.25

0.35 = x / $14.25

x = $14.25 × 0.35

Apply the multiplication operation, and we get

x = 4.9875

So sale price = markup + cost

So sale price = $4.9875 + $14.25

So sale price = $19.237

Thus, the markup rate will be 35% when the cost of the book is $14.25 and sells for $19.237.

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PLEASE HELP for my math class

Answers

Answer:

  $134.49

Step-by-step explanation:

Multiply the rate by the salary:

  7.65% × $1758 = $134.49

Tyler's employer should deduct $134.49.

does anyone know this ?

Answers

Answer:

Equation: 12 + 3x = 30

Solution: x = 6

Step-by-step explanation:

12 + 3x = 30

X stands for how many hours she rented it for. You want to solve for x, so get x by itself.

12 + 3x = 30

-12           -12

---------------------

3x = 18

Divide both sides by 3

3/3x = 18/3

x = 6

what is the equation of the line shown in this graph

Answers

Notice that the line on this graph is a flat line or a horizontal line.

When you are asked to write the equation of a horizontal line,

your equation will always be in the form of y = a number.

When y = a number, the graph is a horizontal line or a

flat line whose y-intercept is equal to that number.

Since the y-intercept is the point where the line crosses the y-axis and our line crosses it at the point (0, -1), the equation of this line is y = -1.

Can you work out this math puzzle?

Answers

Triangle=10
Circle=5
Square:3.5
Half square:1.75
Answer to ?:26.25

The value of the puzzle is 17

The value of the triangle :

30/3 = 10

Value of Circle :

10/2 = 5

Value of whole yellow square :

8/2 = 4

Value of half-yellow square :

4/2 = 2

Using the above information:

Triangle + Circle + half-square

10 + 5 + 2 = 17

Therefore, the solution to the puzzle is 17

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Pls answer this question I give brainliest thank you! Number 2

Answers

Answer:

Step-by-step explanation:

Answer:

D. 625

Step-by-step explanation:

If the side length for each block is 2 1/2 then two blocks together make 5 so 4 blocks going up makes the height 10 and two blocks for the width make 5 and the 5 blocks on the bottom going across for length make 12 1/2 and 5*10*12 1/2= 625

Which expressions are equivalent to -6.3x - 4.2?
-4.7 - 2.3x + 0.5 - 4x
-5.3x - 4.2 - x
-3.4 - 6.3x - 0.8
-6.2x - 4.2
-4.2x - 6.3
-3.7 - 5.3x + 0.5

multiple choice.

Answers

Answer:

(1): -4.7 - 2.3x + 0.5 - 4x

(2):-5.3x-4.2-x

(3):-3.4-6.3x-0.8

Step-by-step explanation:

By Collecting like terms and adding the answer I get -6.3x - 4.2

(1):-4.7-2.3x+0.5-4x

Collect like terms

-2.3x-4x-4.7+0.5

-6.3x-4.2

(2):-5.3x-4.2-x

Collect like terms

-5.3x-x-4.2

-6.3x-4.2

(3): -3.4-6.3x-0.8

Collect like terms

-6.3x-3.4-0.8

-6.3x-4.2

Answer:

The first 3 are equivalent the last 3 aren't.

Step-by-step explanation:

What is more 7 9/10 or 7 4/5?

Answers

Answer:

7 9/10

Step-by-step explanation:

7 9/10 is more than 7 4/5

Hector invests $20,000 at age 21. He hopes the investment will be worth $200,000 when he turns 40. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.

Answers

Answer:

12.12%

Step-by-step explanation:

We have that the formula is given by:

A = p * e ^ (r * t)

From here, we know that A = 200000; p = 20000 and the time we can calculate 40 - 21 = 19

if we replace we have:

200000 = 20000 * e ^ (19 * r)

we must calculate r:

e ^ (19 * r) = 200000/20000

e ^ (19 * r) = 10

19 * r = ln 10

r = ln 10/19

r = 0.1212

In other words, the rate of growth is 12.12%

Answer:

12.1%

Step-by-step explanation:

A boathouse costs $2750 a month to operate, and it spends $650 each

month for every boat that it docks. The boathouse charges a monthly fee of

$900 to dock a boat. If n is the number of boats, which equation represents

the profit function of the boathouse?

O A. p = 2750n + 250

O B. p= 900n + 2750

O c. p = 250n- 2750

O D. p = 650n + 2750

Answers

Answer: P=250n-2750

Step-by-step explanation:

The profit function of the boathouse is given as follows p = 250n- 2750.

What is the profit function?

The profit function is a mathematical function that reflects a company's or business's profit as a function of the number of products or services produced and sold.

The revenue generated by the boathouse with n boats is given by the monthly fee per boat multiplied by the number of boats, which is $900n.

The total cost to operate the boathouse with n boats is the fixed cost of $2750 plus the variable cost of $650 per boat, which is $2750 + $650n.

Therefore, the profit function of the boathouse is given by the revenue minus the cost:

p = 900n - (2750 + 650n)

Simplifying this expression, we get:

p = 250n - 2750

Thus, the answer is (c) p = 250n - 2750.

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In how many ways can a member of a hiring committee select 3 of 12 job applicants for further consideration?

Answers

Answer: 220

Step-by-step explanation:

When we wanto to create a group of K elements for a set of N elements (where the order of the K elements does not matter, so we do not considerate the permutations of the K elements), the number of possible combinations is:

[tex]C = \frac{N!}{(N - K)!*K!}[/tex]

Here N = 12 and K = 3

[tex]C = \frac{12!}{9!*3!} = \frac{12*11*10}{3*2} = 220[/tex]

So there are 220 possible combinations

Answer:

220

Step-by-step explanation:

A music professor offers his 40 students the option of coming to an additional rehearsal session the week before their juries (musical final exams.) In order to decide whether these extra sessions actually help students, he keeps track of who attends them and compares their jury scores to those of students who did not schedule extra sessions. This study is a(n): A) matched pairs design. B) randomized block design. C) nonrandomized experiment. D) observational study. E) completely randomized experiment.

Answers

Answer:

D. Observational Study

Explanation:

An observational  study is one in which all the participants are subjected to a common treatment and then compared to people who did not receive the same treatment. This is the case with the students who where subjected to the same treatment; an additional rehearsal session. They are then observed by the professor and compared to those who did not participate in the experiment.  

This is also an example of a cohort observational study. A cohort observational study is one in which all the participants have a common uniting factor. They are made to undergo a treatment and then compared to those who did not receive the treatment. This type of study  is subject to bias because a positive or negative result might be because of other factors not related to the study.

A flagpole casts a shadow that is 21m long when the angle between the suns ray and the ground is 48. Determine the height of the flagpole to the nearest metre

Answers

Answer:

  23 m

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationships between angle functions and side measures in a right triangle. The geometry of this problem can be modeled as a right triangle with one leg (h) equal to the height of the pole, and one leg (21 m) that is the shadow length on the ground. The angle of the sun's rays is the angle opposite the h leg, so we can use ...

  Tan = Opposite/Adjacent

  tan(48°) = h/(21 m)

  h = (21 m)tan(48°) ≈ 23.32 m

The height of the flagpole is about 23 meters.



If V = 15 cm, W = 20 cm, X = 25 cm, Y = 7 cm, and Z = 22 cm, what is the perimeter of the object?
A.
53 cm
B.
64 cm
C.
118 cm
D.
78 cm

Answers

Answer:

Sum of all the sides.

Step-by-step explanation:

Perimeter is the sum of the distance in length or width, or height or circumference of all the sides of an object.

Therefore the sum total of the given sides V, W, x ,Y, Z are;

15 +20 + 25 + 7 + 22 = 89cm

Since a picture isn't available to know which sides of the objects can be added.

What is the midline equation of the function h(x) = 5 sin(4.x– 2) – 3?
y=

Answers

Answer:

  y = -3

Step-by-step explanation:

The midline value is the added constant, -3. The equation for the line is ...

  y = -3

can someone help me with my homework please!!!​

Answers

Answer:

c

Step-by-step explanation:

You can either try each answer on the table above, or find the slope then find the function/equation.

c-y1=s(n-x1)

(x1,y1) being any pair from the table and s being the slope.

Determines the length of the chord intercepted by the straight line of equation y = -4x + 8 on the parabola of equation y = -3x^2 + 5x + 2.

Answers

Answer:

Let's work out the intercepted points:

-4x + 8 = -3x^2 + 5x + 2

<=>

3x^2 - 9x + 6 = 0

<=>

x^2 - 3x + 2 = 0

<=>

(x - 1)(x - 2) = 0

<=>  

x = 1 => y = -4 x 1 + 8 = 4 => A(1, 4)

and

x = 2=> y = -4 x 2 + 8 = 0 =>B(2, 0)

Then, length of chord AB is calculated by:

L = sqrt [(2 - 1)^2 + (0 - 4)^2)] = ~4.123

The fair spinner shown in the diagram above is spun.
Work out the probability of getting a factor of 10.
Give your answer in its simplest form.


Answers

Answer:

The answer is "0.2"

Step-by-step explanation:

Given value:

factor = 10

The amount of two divided by the number of options. When both fours and eight gaps are available, that probability can be defined as follows:

[tex]\Rightarrow \frac{2}{10}\\\\\Rightarrow \frac{1}{5}\\\\\Rightarrow 0.2\\[/tex]


Caroline is making a triangular flag with a base of 10 inches and a height of 8 inches. What is the
area of the flag?

Answers

Answer:

take your base x height and / 2. 10x8=80/2=40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 19 specimens of a particular species, 6 resprouted after fire. Estimate with 96% confidence the proportion of all shrubs of this species that will resprout after fire. Interval: .1884 to

Answers

The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.

Here, we have,

To estimate the proportion of all shrubs of this species that will resprout after fire with 96% confidence, we will use the formula for a confidence interval for a proportion.

The formula for the confidence interval for a proportion (p) is given by:

CI = p ± Z * √(p * (1 - p) / n)

where:

CI is the confidence interval

p is the sample proportion (resprouted specimens / total specimens)

Z is the critical Z-score corresponding to the desired confidence level (96% confidence level corresponds to a Z-score of approximately 1.750)

n is the sample size (total number of specimens)

Given information:

Total number of specimens (n) = 19

Number of specimens that resprouted after fire = 6

Now, calculate the sample proportion (p):

p = (number of specimens that resprouted) / (total number of specimens)

p = 6 / 19 ≈ 0.3158 (rounded to four decimal places)

Now, calculate the critical Z-score for a 96% confidence level (use a Z-table or calculator):

Z ≈ 1.750

Now, calculate the margin of error (E):

E = Z * √(p * (1 - p) / n)

E = 1.750 * √(0.3158 * (1 - 0.3158) / 19)

E ≈ 0.1884 (rounded to four decimal places)

Finally, calculate the confidence interval:

CI = p ± E

CI = 0.3158 ± 0.1884

The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.

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Apply the distributive property to factor out the greatest common factor of all three terms. Explanation: 9-12x+6y what is the answer??

Answers

Answer: [tex]3(3-4x+2y)[/tex]

Step-by-step explanation:

[tex]9-12x+6y[/tex]

[tex]3(3-4x+2y)[/tex]

If 5 potatoes together have a mass of 1 kilogram and 8 pears together have a mass of 1200 grams, which has the greater mass, a potato or a pear?

Answers

The Potato has more mass

What is a Regression equation

Answers

Answer:

Regression equations can help you figure out if your data can be fit to an equation.This is extremely useful if you want to make predictions from your data- either future predictions or indications of past behavior.For example,you might want to know what your savings are going to be worth in the future.There are several types of regression equations,some of the more common include exponential and simoke linear regression.In elementary statistics,the regression equation you are most likely to come across is the linear form.

Problem 1.) A researcher claims that 96% of college graduates say their college degree has
been a good investment. In a random sample of 2000 graduates, 1500 say their college degree has
been a good investment. At a = 0.05 is there enough evidence to reject the researcher's claim?

Answers

Answer:

 |Z| = |-52.5|  = 52.5 > 1.96 at 0.05 level of significance

 Null  hypothesis is rejected

We rejected the researcher's claim

A researcher do not claims that 96% of college graduates say their college degree has been  a good investment.

Step-by-step explanation:

Explanation:-

Given data A researcher claims that 96% of college graduates say their college degree has  been a good investment.

Population proportion 'P' = 0.96

                                       Q = 1-P = 1- 0.96 = 0.04

In a random sample of 2000 graduates, 1500 say their college degree has

been a good investment.

Sample proportion

                       [tex]p^{-} = \frac{x}{n} = \frac{1500}{2000} = 0.75[/tex]

Level of significance  ∝ = 0.05

[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]

Test statistic

                        [tex]Z = \frac{p^{-} - P }{\sqrt{\frac{PQ}{n} } }[/tex]

                        [tex]Z = \frac{0.75 - 0.96 }{\sqrt{\frac{0.96 X 0.04}{2000} } }[/tex]

                        [tex]Z = \frac{-0.21}{0.00435} = -52.5[/tex]

    |Z| = |-52.5|  = 52.5 > 1.96 at 0.05 level of significance

  Null  hypothesis is rejected

  We rejected the researcher's claim

Conclusion:-

A researcher do not claims that 96% of college graduates say their college degree has been  a good investment.

     

The measures of the angles of a triangle are 25 degrees, 87 degrees, and 68 degrees. Is the triangle acute, right, or obtuse?

Answers

Answer:

their all less than 90 degress so its acute

Step-by-step explanation:

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