The process standard deviation is , and the process control is set at plus or minus standard deviation . Units with weights less than or greater than ounces will be classified as defects. What is the probability of a defect (to 4 decimals)
Answers
a)The probability of a defect is 0.1836 and total number of defect found would be 184 .
b)The probability of a defect is 0.1770 and total number of defect found would be 177.
The probability of a defect, we can use the normal distribution with the given mean weight, process standard deviation, and process control limits.
The process control limits are set at plus or minus 2.4 standard deviations.
The lower control limit is 12 - (2.4 × 0.14) = 11.664 ounces .
The upper control limit is 12 + (2.4 × 0.14) = 12.336 ounces.
The probability of a defect, we need to calculate the area under the normal distribution curve outside of this range. We can use a standard normal distribution table or a statistical software to find the corresponding probabilities.
Let's calculate the probability of a defect:
Probability of a defect = Probability (weight < 11.664 or weight > 12.336) = Probability (weight < 11.664) + Probability (weight > 12.336)
Since the normal distribution is symmetric, we can calculate the probability of weight less than 11.664 and multiply it by 2 to get the total probability of a defect.
Using a standard normal distribution table or a statistical software, we find that the probability of weight less than 11.664 (Z-score = (11.664 - 12) / 0.14) is approximately 0.0918.
Therefore, the probability of a defect is 2 × 0.0918 = 0.1836 (rounded to 4 decimals).
In a production run of 1000 parts, we can estimate the number of defects by multiplying the probability of a defect by the number of parts:
Number of defects = Probability of a defect × Number of parts = 0.1836 × 1000 = 183.6
Rounding to the nearest whole number, approximately 184 defects would be found.
b. If the process standard deviation is reduced to 0.12, while the process control limits remain the same, we can repeat the same calculations.
The lower control limit is 12 - (2.4 × 0.12) = 11.712 ounces, and the upper control limit is 12 + (2.4 × 0.12) = 12.288 ounces.
Probability of a defect = Probability (weight < 11.712 or weight > 12.288) = Probability (weight < 11.712) + Probability (weight > 12.288)
Using a standard normal distribution table or a statistical software, we find that the probability of weight less than 11.712 (Z-score = (11.712 - 12) / 0.12) is approximately 0.0885.
Therefore, the probability of a defect is 2 × 0.0885 = 0.1770 (rounded to 4 decimals).
In a production run of 1000 parts, the estimated number of defects would be:
Number of defects = Probability of a defect × Number of parts = 0.1770 × 1000 = 177
Rounding to the nearest whole number, approximately 177 defects would be found.
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The question is incomplete the complete question is :
Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 12 ounces. a. The process standard deviation is 0.14, and the process control is set at plus or minus 2.4 standard deviations. Units with weights less than 11.664 or greater than 12.336 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of 1000 parts, how many defects would be found to the nearest whole number)? b. Through process design improvements, the process standard deviation can be reduced to 0.12. Assume the process control remains the same, with weights less than 11.664 or greater than 12.336 ounces being classified as defects. What is the probability of a defect (to 4 decimals)? In a production run of 1000 parts, how many defects would be found to the nearest whole number)?
Related Questions
When I have walked 20% of the way to school, I have 1200 metres more to walk than when I have 20% of the walk remaining.
How far, in metres, is it from my home to my school?
Answers
Answer:
The house is 2000 meters from the school.
Step-by-step explanation:
Given that, when I have walked 20% of the way to school, I have 1200 meters more to walk than when I have 20% of the walk remaining, to determine how far, in meters, is it from my home to my school the following calculation has to be done:
100 - 20 = 80
80 = 20 + 1200
80 - 20 = 1200
60 = 1200
1200/60 = 20
20 x 100 = 2000
Therefore, the house is 2000 meters from the school.
find the perimeter of a rectangular frame with sides of 4x - 1 and 6x +5
Answers
Answer:
p = 20x
hope it's helpful ❤❤❤❤❤
THANK YOU.
Answer: 20x+8
Step-by-step explanation
Got it correct!
can someone help me on these 3 problems please ! and explain aswell ??
Answers
Answer:
try finding slope
Step-by-step explanation:
Look at the following shapes:
A group of fives shapes. An isosceles trapezoid labeled P, a parallelogram which is not a rectangle or rhombus, labeled Q, a square labeled R, a trapezoid with one vertical side labeled S and a rhombus which is not a square, labeled T.
The shapes were sorted, and Shape R and Shape S were put in the same group.
Which statement shows a rule that could have been used to group these two shapes? (1 point)
a
Shapes without any right angles
b
Shapes with exactly one pair of parallel sides
c
Shapes without parallel line segments
d
Shapes with perpendicular line segments
Answers
Shape R and Shape S were put in the same group because they are the shapes with perpendicular line segments. Therefore the correct option is option D.
Shape S, a trapezium with one vertical side, and Shape R, a square, both have perpendicular line segments. All of the sides of a square are perpendicular, while one of the non-parallel sides of a trapezium with a vertical side is perpendicular to the base.
Reasons for ruling out other options
Option A, "Shapes without any right angles," is incorrect because Shape R (a square) has four right angles.
Option B, "Shapes with exactly one pair of parallel sides," is incorrect because Shape S (a trapezoid with one vertical side) has only one pair of parallel sides, while Shape R(a square) has two pairs of parallel sides.
Option C, "Shapes without parallel line segments," is also incorrect because all the other shapes P, Q, and T have parallel line segments.
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A dealership is selling new electric cars. The factory gives a $3000 rebate to college students, and the dealership gives college students a 15% discount. Write a function d(x) that represents a car price after a discount from the dealership
Answers
A function d(x) that represents a car price after a discount from the dealership is d(x)=0.85x+3000.
Given that, the factory gives a $3000 rebate to college students, and the dealership gives college students a 15% discount.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, a function d(x) that represents a car price after a discount from the dealership.
Let the cost of new electric cars be x.
So, discount = 15% of x
=0.15x
Selling price = x-0.15x=0.85x
Now, d(x)=0.85x+3000
Therefore, a function d(x) that represents a car price after a discount from the dealership is d(x)=0.85x+3000.
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You randomly survey men and women about whether they plan to watch a football game on Sunday afternoon. A total of 40 men plan to watch a football game and a total of 17 women do not plan to watch a football game. A total of 45 women are surveyed. A total of 33 people do not plan to watch a football game. How many people did you survey?
Answers
Answer: 101
Step-by-step explanation:
45 women total
17 women will not watch the game
So 33 people did not want to watch the game and 17 are women
33-17 = 16 men who won’t watch the game
So 40 men who will and 16 men who won’t equals 56 men and 45 women
56+45= 101
How do you find the remainder when a polynomial in x is divided by a binomial of the form XR?
Answers
There are two ways to find the remainder when a polynomial in x is divided by a binomial of the form x-r, the use of synthetic division or calculate P(r).
Synthetic division
The Synthetic division is a shortcut way of polynomial division, especially if we need to divide it by a linear factor. It is generally used to find out the zeroes or roots of polynomials and not for the division of factors.
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
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The cross section of a prism is an n sided polygon.
Circle the number of edges that the prism has.
2n
n+2
n+ 3
3n
Answers
The number of edges that the prism has is
n + 2What does a prism's cross section look like?When a plane intersects a prism, the shape formed is known as the cross section. The cross section of the prism will have the same form as the base if it is divided by a plane that runs horizontally and parallel to the base.
A prism is a 3-dimensional object with two congruent and parallel bases (which are polyggonal) connected by rectangular lateral faces. The number of edges of a prism is equal to the sum of the number of edges of the two bases and the number of lateral faces.
Each base of the prism has n edges, so the two bases together have 2n edges. The number of lateral faces of the prism is equal to the number of edges of one of its bases, so there are n lateral faces. Each lateral face has 4 edges, so the total number of edges of the lateral faces is 4n.
Therefore, the total number of edges of the prism is equal to the sum of the number of edges of the two bases (2n) and the number of lateral faces (4n), which is 2n + 4n = 6n.
In conclusion, the cross section of a prism is an n-sided polygon and the prism has n + 2 edges.
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8. Jake wants to buy the foam gymnastic block shown. If the
foam used to make the gymnastic block costs $24.99 per
cubic foot, what is the cost of this block, to the nearest
dollar?
Answers
After answering the provided question, we can conclude that Therefore, cuboid the cost of the gymnastic block is $225.
what is cuboid?A cuboid is a solid or three-dimensional shape in geometry. A cuboid is a convex polyhedron with 8 coordinates, 12 sides, but rather 6 rectangular faces. A cuboid is another name for it. A box is a cuboid because it has six square faces. Objects unearthed in boxes include bricks and books. The following are the primary distinctions between cubic and cubic: In contrast to a cube's rectangular faces, the faces of a capsule are perfectly straight and equal in size. But even though the structures of both the cube and cuboid are similar, they differ significantly in terms of side length, horizontal, and area.
the volume of the block is:
Volume = length x width x height
Volume = 2 ft x 3 ft x 1.5 ft
Volume = 9 cubic feet
Now, to find the cost of the block, we can multiply its volume by the cost of foam per cubic foot:
Cost of block = Volume x Cost per cubic foot
Cost of block = 9 cubic feet x $24.99 per cubic foot
Cost of block = $224.91
Therefore, the cost of the gymnastic block is $225.
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It distance Runner is running an 18 mile race so far she has her own 43% of the race would be the best way to estimate the number of miles around her as run so far by the 40% of 10 to 40% of 25 50% of 10 and 50% of 20
Answers
Answer:
40% of 10
Step-by-step explanation:
I believe the answer would be 40% of 10.
Hope this helps, if so please mark the brainliest, peace and love
Answer:
50%
Step-by-step explanation:
The more it was showed so its like 50%.
How do you find the number of distinguishable permutations of the group of letters: A, A, G, E, E, E, M?
Answers
In order to find the number of distinguishable permutations of the group of letters A, A, G, E, E, E, M, we can use the following formula:
The number of permutations = n! / (n1! n2! ... nk!), where n is the total number of objects to be arranged, and n1, n2, ..., nk are the numbers of objects that are identical to one another.
For this problem, we have 7 letters with 2 A's, 3 E's, and 1 G and 1 M letter.
Using the formula above, we can find the number of distinguishable permutations: 7! / (2! 3! 1! 1!) = (7 × 6 × 5 × 4 × 3 × 2 × 1) / [(2 × 1) × (3 × 2 × 1) × (1 × 1) × (1 × 1)] = 2520
Therefore, there are 2520 distinguishable permutations of the group of letters A, A, G, E, E, E, M.
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If a1 = -9, and an = -6 an-1, list the first five terms of an: . {a1, a2, a3, a4, a5}
Answers
The first five terms of the sequence are {-9, 54, -324, 1944, -11664}.Hence, the first five terms of the sequence are {-9, 54, -324, 1944, -11664}.
Given that a1 = -9 and an = -6an-1 to find the first five terms of an: {a1, a2, a3, a4, a5}
We have to use the formula an = -6 an-1 to find the next terms.
The first term a1 is given to us. So, a1 = -9
We can use the formula an = -6an-1 to find the next term using a1= -9 an1 = -6 * a1 = -6 * (-9) = 54
Thus the first two terms of the sequence are {-9, 54}.
We can use the formula an = -6an-1 to find the third term an2 = -6 * an1= -6 * 54 = -324
Thus the first three terms of the sequence are {-9, 54, -324}.
We can use the formula an = -6an-1 to find the fourth term an3 = -6 * an2= -6 * (-324) = 1944
Thus the first four terms of the sequence are {-9, 54, -324, 1944}.
We can use the formula an = -6an-1 to find the fifth term an4 = -6 * an3= -6 * (1944) = -11664
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Can someone explain how to solve
———-
-2x+2y=2
-x-2y=1
————-
by elimination?
Answers
Answer:
when using elimination you "eliminate one variable by adding the equations", so basically in this equation 2y-2y cancel out when you add the equations together. so, you'll find x first. once you find the value of x, then you plug x into one of the equations to find the ordered pair solution, which happens to be (-1,0) in this solution.
Step-by-step explanation:
i hope this helps :)
Alyssa is tracking the growth of a plant.
• The plant grows c inches in the first week and n inches
in the second week.
Enter an equation to show that the plant grows 2 inches more
in the second week than in the first week.
Answers
An equation to show that the plant grows 2 inches more in the second week than in the first week is n = c + 2.
How to write an equation to show the plant's growth in the second week?In this scenario and exercise, you are required to write a linear equation to model the plant's growth in the second week with respect to the first week.
In order to write a linear equation to describe this situation, we would assign variables to the height of the plant in the first week and the height of the plant in the first week respectively, and then translate the word problem into an algebraic equation (linear equations) as follows:
Let the variable c represent the height of the plant in the first week.Let the variable n represent the height of the plant in the second week.Since the plant grew c inches in the first week, a linear equation to describe the height of the plant in the second week is given by;
n = c + 2
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Mona is purchasing a shirt. the total cost, c, of the shirt will be the price of the shirt, p, increased by 6% of the price of the shirt for sales tax. write an equation that represents the total cost of the shirt?
Answers
The equation representing total cost of the shirt is c = 1.06p.
As per the question, we are representing the total cost of the shirt as c and price of the shirt as p.
Calculating sales tax on the shirt -
Sales tax = p × 6%
Converting percentage to fraction and hence decimal form
Sales tax = p× 6/100
Sales tax = 0.06p
Forming the equation now -
Total cost = price of the shirt + sales tax on the shirt
c = p + 0.06p
Performing addition on Right Hand Side of the equation to find the equation representing total cost
c = 1.06p
Therefore, the equation representing the total cost of the shirt is c = 1.06p.
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A deli has two platters of sandwiches. The first platter costs $33
and you get 2 turkey sandwiches and 3 roast beef sandwiches.
The other platter costs $32 and you get 3 turkey sandwiches and
2 roast beef sandwiches. Let x represent the cost of each
turkey sandwich and y represent the cost of each
roast beef sandwich. What is the system of linear equations
for the given scenario? What is the cost of each sandwich?
Answers
From the first platter, which costs $33 and contains 2 turkey sandwiches and 3 roast beef sandwiches, we can write the equation:
2x + 3y = 33
From the second platter, which costs $32 and contains 3 turkey sandwiches and 2 roast beef sandwiches, we can write the equation:
3x + 2y = 32
Now we have a system of two linear equations in two variables:
2x + 3y = 33
3x + 2y = 32
To solve for x and y, we can use the method of elimination. Multiplying the first equation by 2 and the second equation by -3, we get:
4x + 6y = 66
-9x - 6y = -96
Adding these equations, we get:
-5x = -30
Dividing both sides by -5, we get:
x = 6
Now we can substitute x = 6 into either of the original equations to solve for y. Using the first equation, we get:
2(6) + 3y = 33
12 + 3y = 33
3y = 21
y = 7
Therefore, each turkey sandwich costs $6 and each roast beef sandwich costs $7.
[PLEASE HELP ILL GIVE BRAINLIEST
PLEASE SHOW WORK
Answers
Please help this is algebra!
Answers
Answer:
7 nickels
20 dimes
5 quarters
Step-by-step explanation:
n=nickels. d=dimes. q=quarters
n+d+q=32
0.05n+0.1d+0.25q=3.60
d=8+n+q
Solve for number of dimes:
d-8=8-8+n+q
d-8=n+q
d-d-8=n+q-d
-8=n+q-d
32=n+q+d
- (-8=n+q-d)
32 - (-8) = n-n + q-q + d-(-d)
32 + 8 = d + d
40 = 2d
d = 20 => simplify
20=8+n+q ==> substitute 20 for d (d=8+n+q)
20-8 = 8-8+n+q
n+q = 12
0.05n+0.1(20)+0.25q=3.60 ==> substitute 20 for d
0.05n + 2 + 0.25q = 3.60
(0.05n + 2 + 0.25q = 3.60)*100 ->remove the decimals by multiplying by 100
5n + 200 + 25q = 360
5n + 200 - 200 + 25q = 360 - 200
5n + 25q = 160
Solve for number of quarters:
(5n + 25q)/5 = 160/5 ==> simplify the equation
n + 5q = 32
- (n + q = 12)
n-n + 5q-q = 32-12
0 + 4q = 20
4q = 20
q = 5 ==> simplify
Solve for number of nickels:
n+20+5=32 ==> plug in 20 for d and 5 for q (n+d+q=32)
n+25=32
n+25-25=32-25 ==> solve for n
n=7 ==> simplify
n=7: 7 nickels
d = 20: 20 dimes
q = 5: 5 quarters
What is the square root of the quantity x plus 4 minus 3 equals 1
Answers
Answer:
sqrt(x+4)-3=1 x equals 12 bottom answer
Step-by-step explanation:
sqrt,(x+4)=4
x+4 =16 x=12 please add me and mmsrk brainest
1. A department of motor vehicles office claims that the mean wait time is less than 14 minutes. A random sample of 10 people has a mean wait time of 13 minutes with a standard deviation of 3.5 minutes. At = 0.10, test the office’s claim. Assume the population is normally distributed.
Answers
The hypothesis testing for a random sample of 10 people has a some mean wait time and standard deviations is provided,
H₀ : μ = 14min
Hₐ : μ <14min
After testing we get , P-value > α which implies that we are fail to reject null hypothesis .
So, We don't have sufficient evidence to conclude that the mean wait time is less than 14 minutes at 0.1 level of significance.
Consider the null and alternative hypothesis as:
H₀ : μ = 14min
Hₐ : μ < 14min
α = 0.1
we have given that,
Sample mean, X-bar = 13 minutes
Sample size, n = 10
standard deviations, σ = 3.5 minutes
test Statistic:
t = ( X-bar - μ )/σ/√n
t = ( 13-14)/3.5/√10 )
=> t = -1/3.5/3.16
=> t= -1/1.11
=> t= -0.90
degree of freedom df = n-1 = 10-1 = 9
Using the t-table, the p-value for t = -0.90 and degree of freedom 9 is 0.195..
The result is not significant because
p-value > α (0.10)
Decision: fail to reject the null hypothesis, H₀.
We don't have sufficient evidence to conclude that the mean wait time is less than 14 minutes at 0.1 level of significance.
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Explain if the triangles below are congruent or not and explain why you think that.
Answers
In this picture, we have the triangles with two common sides and one common angle. However, they are not congruent, as they do not follow any of the congruence theorems. The congruence theorem with two sides and an angle is the SAS(Side-Angle-Side). However, the angle has to be the angle between the two sides, which does not happen in this case.
Find the value of x
A. 40 degrees
B. 80 degrees
C. 90 degrees
D. 160 degrees
Answers
Answer:
b 80 deg
Step-by-step explanation:
The measure of an arc of a circle equals the measure of its central angle.
Since the central angle has measure 80 degrees, x is also 80 degrees.
Name a career in which one would have to use the Pythagorean Theorem. Give an example of when, where, and how it would be used.
FULL EXPLANATION NEEDED
Answers
Answer:
Engineers use the Pythagorean Theorem to figure out measurements of objects.
A man bought an article for Rs 225 and sold it at a gain of 15%. how much was his profit?
Answers
Answer:
225 x 0.15 = 33.75 profit
Step-by-step explanation:
Answer:
Profit: Rs 33.75
Step-by-step explanation:
His profit was 15% of Rs 225, which comes to 0.15(Rs 225), or Rs 33.75
Jonathan did 180 situps in 45 second. How many situps did Jonathan do in one second?
Answers
Answer:
180/45 = 4/1, he did 4 situps in 1 second.
Answer:
4 situps
Step-by-step explanation:
180 divided by 45s = 4 situps
s = seconds
Dilate quadrilateral abcd using center b and scale factor 1/2
Answers
The dilated quadrilateral, using center B and a scale factor of 1/2, is A'B'C'D'.
To dilate a quadrilateral ABCD using center B and a scale factor of 1/2, we can follow these steps:
Draw line segments from the center of dilation (B) to each vertex of the quadrilateral (A, C, and D).
Measure the distance from B to each vertex (AB, BC, BD) and multiply each distance by the scale factor (1/2).
From the endpoints of the original line segments, construct new line segments with the scaled distances obtained in the previous step.
Connect the endpoints of the newly constructed line segments to form the dilated quadrilateral A'B'C'D'.
The resulting quadrilateral A'B'C'D' will be a scaled-down version of the original quadrilateral ABCD, with center B as the center of dilation and a scale factor of 1/2.
Note: Since I am a text-based AI and cannot provide visual illustrations, it would be helpful to refer to a geometric software or draw the quadrilateral on paper to visualize the steps described above.
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WILL GIVE BRAINLIEST TO ANYONE WHO ANSWERS!!
Quadrilateral OPQR is inscribed inside a circle as shown below. What is the measure of angle P? You must show all work and calculations to receive credit. (10 points) Circle N is shown with an inscribed quadrilateral labeled OPQR. O is labeled 2x degrees. P is labeled y degrees. Q is labeled 2
Answers
Answer:
The measure of angle P is 43°
Step-by-step explanation:
If a quadrilateral is inscribed inside a circle, the sum of opposite angles are always equal to 180 degrees.
The angle POR is opposite to the angle PQR, and the angle OPQ is opposite to the angle ORQ.
So we have that:
mOPQ + mORQ = 180°
y + 3y + 8 = 180
4y = 172
y = 43°
So the measure of angle P is 43°.
Please help. Also it’s a picture
Answers
===================================
Work Shown:
A = P*(1+r/n)^(n*t)
A = 500*(1+0.05/4)^(4*3)
A = 580.3772588615
A = 580.38
A t-bill with face value $10,000 and 87 days to maturity is selling at a bank discount ask yield of 3. 4%.
Answers
The bank discount ask yield on a Treasury bill with a face value of $10,000 and 87 days to maturity is 3.4%.
Treasury bills are short-term debt instruments issued by the government to raise funds. They are sold at a discount to their face value and mature at par. The bank discount yield is the annualized rate of return based on the discount price and face value. To calculate the yield, we use the formula:
Bank Discount Yield = (Discount / Face Value) * (360 / Days to Maturity)
In this case, the discount is the difference between the face value and the price at which the T-bill is selling. Let's assume the price is P. The discount is then calculated as: Discount = Face Value - P.
Substituting the given values, we have: Discount = $10,000 - P.
The bank discount yield is 3.4%, which means:
0.034 = (Discount / $10,000) * (360 / 87)
Solving for Discount, we find Discount ≈ $139.08.
Substituting this value back into the Discount formula, we can find the price P ≈ $9,860.92.
Therefore, the T-bill is selling at a price of approximately $9,860.92, and the bank discount ask yield is 3.4%.
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A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution: Price: $10.00 $12.50 $15.00 Probability: 0.35 0.40 0.25 How much should the lab budget for next year's rat orders be, assuming this distribution does not change
Answers
The lab should budget for the next year's rat orders be $63,700.00.
The lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.
The prices for 100 rats follow the given distribution:
Price ($): 10.00, 12.50 , 15.00
Probability: 0.35 0.40 0.25
Mean price per 100 rats can be calculated using the expected value formula,
μx = ∑ [ xi × P(xi) ]
where
μx = mean value,
xi = price,
P(xi) = probability of xi
Mean price per 100 rats:
μx = (10.00 × 0.35) + (12.50 × 0.40) + (15.00 × 0.25)
μx = 3.50 + 5.00 + 3.75
μx = $12.25
The mean price per 100 rats is $12.25.
Hence, the cost of 100 rats is $12.25.
Therefore, the lab should budget for the next year's rat orders:
$12.25 × 100 × 52
= $63,700.00
The lab should budget for the next year's rat orders be $63,700.00.
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