A company employs two shifts of workers. Each shift produces a type of gasket where the thickness is the critical dimension. The average thickness and the standard deviation of thickness of shift 1, based on a random sample of 30 gaskets, are 10.53mm and 0.14mm. The similar figures for shift 2, based on a random sample of 25 gaskets, are 10.55mm and 0.17mm. Let µ1-µ2 be the mean difference in thickness between shifts 1 and 2.
a) Find a 95% confidence interval for µ1-µ2.
b) Based on your answer to part a, are you convinced that the gaskets from shift 2 are, on average, wider than those from shift 1? Why or why not?
c) How would your answers to parts a and b change if the sample sizes were instead 300 and 250?
Answers
Answer:
(−0.103371 ; 0.063371) ;
No ;
( -0.0463642, 0.0063642)
Step-by-step explanation:
Shift 1:
Sample size, n1 = 30
Mean, m1 = 10.53 mm ; Standard deviation, s1 = 0.14mm
Shift 2:
Sample size, n2 = 25
Mean, m2 = 10.55 ; Standard deviation, s2 = 0.17
Mean difference ; μ1 - μ2
Zcritical at 95% confidence interval = 1.96
Using the relation :
(m1 - m2) ± Zcritical * (s1²/n1 + s2²/n2)
(10.53-10.55) ± 1.96*sqrt(0.14^2/30 + 0.17^2/25)
Lower boundary :
-0.02 - 0.0833710 = −0.103371
Upper boundary :
-0.02 + 0.0833710 = 0.063371
(−0.103371 ; 0.063371)
B.)
We cannot conclude that gasket from shift 2 are on average wider Than gasket from shift 1, since the interval contains 0.
C.)
For sample size :
n1 = 300 ; n2 = 250
(10.53-10.55) ± 1.96*sqrt(0.14^2/300 + 0.17^2/250)
Lower boundary :
-0.02 - 0.0263642 = −0.0463642
Upper boundary :
-0.02 + 0.0263642 = 0.0063642
( -0.0463642, 0.0063642)
Related Questions
Howdy! Thanks for stopping by my question! I would really appreciate the help! I've attached the question below. Thanks!
I'd appreciate if you made sure to double check your answers and provide everything the question is asking! INCLUDE ALL STEPS!
Answers
Answer:
a) x = 1 ± (3/7)√7
b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)
Step-by-step explanation:
You want solutions to the relations ...
7 +1/x = 1/(x-2)(x² -4x -12)/(x² -25) ≥ 0a) 7 + ...We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.
\(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)
The roots of the numerator quadratic are found by ...
x² -2x -2/7 = 0 . . . . . divide by 7
x² -2x +1 -9/7 = 0 . . . . add and subtract 1
(x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7
x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root
x = 1 ± (3/7)√7
b) (x² - ...Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.
\(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)
This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.
The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.
The inequality is satisfied for ...
x < -5-2 ≤ x < 56 ≤ xusing the disk method, determine the volume of a solid formed by revolving the region bounded above by the line , on the left by the line , on the right by the curve , and below by the line the about the -axis.
Answers
The volume of a solid formed by revolving the region bounded above by the line is (932π/15)
To use the disk method, we need to integrate over the axis of revolution, which is the y-axis in this case. We can break the solid into vertical disks of thickness dy.
The radius of each disk is given by the distance between the y-axis and the curve \(x = y^2 - 1\). So the radius is:
\(r = y^2 - 1\)
The height of each disk is the difference between the y-coordinate of the top curve y = 3 and the y-coordinate of the bottom curve y = 1. So the height is:
h = 3 - 1 = 2
The volume of each disk is then:
\(dV = \pi r^2h dy\)
Substituting r and h, we have:
\(dV = \pi (y^2 - 1)^2 (2) dy\)
To find the total volume, we integrate over the range of y from 1 to 3:
\(V = \int_{1}^{3} \pi(y^2 - 1)^2 (2) dy\)
This integral can be simplified by expanding the squared term:
\(V = \int_{1}^{3} \pi (y^4 - 2y^2 + 1) (2) dyV = 2\pi \int_{1}^{3}(y^4 - 2y^2 + 1) dyV = 2\pi [(1/5)y^5 - (2/3)y^3 + y]^3_1\)
V = \(2\pi [(1/5)(3^5 - 1^5) - (2/3)(3^3 - 1^3) + (3 - 1)]\)
V = 2π [(1/5)(242) - (2/3)(26) + 2]
V = 2π [(242/5) - (52/3) + 2]
V = 2π [(726/15) - (260/15) + 30/15]
V = 2π [(466/15)]
V = (932π/15)
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Note: The full question is
Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = 1, y = 3, x = y^2 - 1.
Archie must travel to a foreign country where a deadly strain of flu has ravaged the population. Already, 21% of the population has succumbed to the flu and died. There is a vaccine, but because the flu is extremely contagious, it spreads quite rapidly, and to date only 16 out of every 20 people have been vaccinated. Thirty-seven percent of those who are not vaccinated die from the flu. Archie has just enough time to be vaccinated before he leaves. What is the probability that Archie will succumb to the flu and die while he is away
Answers
Answer:
The probability that Archie will succumb to the flu and die while he is away is 17%.
Step-by-step explanation:
From the question, we have the following:
P(d) = probability of debt = the population has succumbed to the flu and died = 21%, or 0.21
P(v) = probability of getting vaccinated = 16 out of every 20 people = 16 / 20 = 0.80
P(v') = probability of not got vaccinated = 1 - P(v) = 1 - 080 = 0.20
P(d|v') = probability of not vaccinated and die from the flu = 37%, or 0.37
P(d|v) = probability that Archie will succumb to the flu and die while he is away = ?
This can therefore be estimated using the following equation:
P(d) = [P(d|v) * P(v)] + [P(d|v') * P(v')] ...................... (1)
Substitute the values into equation (1) and solve for P(d|v), we have:
0.21 = [P(d|v) * 0.80] + [0.37 * 0.20]
0.21 = [P(d|v) * 0.80] + 0.074
P(d|v) * 0.80 = 0.21 - 0.074
P(d|v) * 0.80 = 0.136
P(d|v) = 0.136 / 0.80
P(d|v) = 0.17, or 17%
Therefore, the probability that Archie will succumb to the flu and die while he is away is 17%.
Long division: 2/ 2769
Answers
Answer:
1384.5
Step-by-step explanation
Diviseion is just the oppisite of multiplication so you can think to yourself that what times two equals 2769. If you multiply 1384.5 on a calculater you get 2769.
If two sides of a triangle are 6 and 16, what is the range of the possible lengths
of the third side?
Answers
The range of the possible length of the third side is between 10 and 22
How to determine the possible length of the third sideFrom the question, we have the following parameters that can be used in our computation:
Lengths = 6 and 16
The possible length of the third side can be calculated using the triangle inequality theorem
For this triangle, the length of the third side must be greater than
16 - 6 = 10
Also, the length of the third side must be less than
16 + 6 = 22
Hence, the possible length of the third sides is between 10 and 22
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Look at the graph below. Is it a function or not a function? Explain your reasoning.
Answers
825 use each digit once. make the smallest 3digit number
Answers
Step-by-step explanation:
Given: To make smallest 3-digit number of 825.
To find: The smallest 3-digit number of 825.
Solution: We can make the smallest 3-digit number of 825 by separating the numbers and arranging it to ascending order. The given number is 825. ...
Final answer: The smallest 3-digit number of 825 is 258.
hope it helps
Answer:
258
Step-by-step explanation:
We are given 3 numbers:
8 2 5
And we are asked to find the smallest 3 digit number using those 3 digits above.
To make the smallest number, place the numbers in value from least to greatest:
2 5 8
This is your 3 digit number: 258.
Hope this helps! :)
The wheel on a scooter completes 124 revolutions and travels 22.4 meters. What is the diameter of the wheel in mm? Use 3.14 for pi and round to the nearest whole millimeter.
Answers
If wheel on a scooter completes 124 revolutions and travels 22.4 meters then diameter of the wheel is 57 mm
Each revolution of the wheel covers a distance equal to the circumference of the wheel.
The diameter of the wheel "d".
The distance covered in 124 revolutions is:
distance = 124 x circumference
= 124 x pi x d
= 124 x 3.14 x d
We know that this distance is equal to 22.4 meters, so we can set up an equation:
124 x 3.14 x d = 22.4
Simplifying and solving for d:
d = 22.4 / (124 x 3.14)
d = 0.057 meters
As we know that 1 meter is equal to thousand millimeters so multiply by 1000 to get in millimeters
d = 57 millimeters
Therefore, the diameter of the wheel is approximately 57 mm.
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If you toss a 1-6 number cube 60 times, how many times do you expect to toss an even number? Toss a 1-6 number cube 60 times and record the results. Do your results match your expected results? Why or why not? Combine your results with the results of your classmates. What would be the expected number of times for an even number to occur? Do the actual results match the expected numbers?
Answers
Given statement solution is :- The actual combined results with the expected number of 30, we can evaluate whether the actual results from the entire class align with the expected values. If the actual combined results are close to 30, it suggests that the empirical data matches the expected numbers. However, if there is a significant discrepancy, it may indicate variations due to chance or potential biases in the data collection process.
To determine the expected number of times an even number will occur when tossing a 1-6 number cube, we can calculate the probability of getting an even number on each toss and multiply it by the total number of tosses.
A 1-6 number cube has three even numbers (2, 4, and 6) out of a total of six possible outcomes. Therefore, the probability of getting an even number on a single toss is 3/6, which simplifies to 1/2.
To find the expected number of times for an even number to occur in 60 tosses, we multiply the probability of an even number (1/2) by the total number of tosses:
Expected number = (Probability of even number) × (Total number of tosses)
Expected number = (1/2) × 60
Expected number = 30
Hence, we would expect an even number to occur approximately 30 times out of 60 tosses.
When conducting the actual experiment by tossing the 1-6 number cube 60 times and recording the results, the obtained numbers may or may not match the expected results exactly. This is because probability deals with likelihoods, and in any given trial, there can be variation or deviations from the expected value due to chance.
To determine if the actual results match the expected numbers, we need to compare the collected data with the expected value of 30. If the actual results are close to 30, we can say they align with the expected numbers.
Combining the results with the data from classmates would involve collecting their individual recorded results and calculating the average or summing up the number of even occurrences to determine the overall frequency of even numbers.
By comparing the actual combined results with the expected number of 30, we can evaluate whether the actual results from the entire class align with the expected values. If the actual combined results are close to 30, it suggests that the empirical data matches the expected numbers. However, if there is a significant discrepancy, it may indicate variations due to chance or potential biases in the data collection process.
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Cuales don las dos terceras partes de tres medios
Answers
Answer:
una parte entenra
Step-by-step explanation:
\(\frac{3}{2}/\frac{2}{3}\\\\=\frac{3}{2}*\frac{3}{2}\\\\=1\)
She borrows $25.63 from her sister to help pay for the dress. Then Jenny earns $16.33 helping her dad organize his home office. If she gives all the earnings to her sister, Jenny will still owe her sister $
.
Answers
she still owes 9.3$
answer : 9.30$
Step-by-Step-
25.63-16.33=9.30
Jenny still owns $9.30 dollars to her sister.
Hope this helps :)
PLS HURRY WILLL GIVE BRAINLIEST!!!
Which is the simplified form of ( 9c^-9 )^-3 ?
Answers
Answer:
Your answer is B: 1/729c^27
Answer:
b
Step-by-step explanation:
pls give brainliest
What is the main problem with this paragraph
Thesis statement: Stores that resell used video games should offer at least 30 percent of the sale price to sellers.
Main points:
More people will sell used games.
More people will buy new games.
The store will make money.
Conclusion: It just makes sense that happy sellers will sell back more used games They'll also be willing to buy more new games, knowing they can sell them back for a good price. This will all lead to more profit for the store. It is a problem that has a simple solution that will benefit everyone involved.
A. It does not restate the thesis.
B. It does not have a satisfying close.
C. It adds new information.
D. It is missing one of the main points
Answers
Answer:
A
Step-by-step explanation:
It never restates the thesis, in which you are required to in anything resembling a formative, constructed response, or an essay.
A) Divide 160km in the ratio 10:9:13
B) divide 66 in the ratio 6:15:1
Answers
Answer:
A) 50 km : 45 km : 65 km
B) 18:45:3
Step-by-step explanation:
A) 160 km in the ratio 10:9:13
10x+9x+13x= 16032x= 160x= 510:9:3 ⇔ 50 km : 45 km : 65 km
B) 66 in the ratio 6:15:1
6x+15x+x= 6622x=66x=36:15:1 ⇔ 18:45:3
A=
10:9:13
B=
6:15:1
if the overall demand for cheddar cheese goes down, what will probably happen to the price of cheddar ?
Answers
if v varies directly as w and v=8, when w=1/2, find the equation that relates v and w
Answers
Answer:
v=16w
Step-by-step explanation:
v=16w
8=16(1/2)
8=8✔
WILL GIVE BRAINLIST!
The cost for an eighth-grade party is $450 for room rental, entertainment, and decorations, plus $20 per person for food. Tickets for the party are sold for $25. What is the break-even point
A-45 TICKETS
B-90 TICKETS
C-18 TICKETS
D-23 TICKETS
*WILL REPORT LINKS AND IF YOU JUST COMMENT FOR NOTHING*
Answers
Answer:
B. 90 tickets
Step-by-step explanation:
For t tickets sold, we want the revenue equal to the cost.
25t = 450 +20t
5t = 450 . . . subtract 20t
t = 90 . . . . . divide by 5
90 tickets is the break-even point.
___
:D
What are the terms in the expression 6r + 5y +3
Answers
Step-by-step explanation:
Your que. isn't very clear
Please help! Will give 60 points!
Answers
9+20-1
29-1
28
So the answer would be 28
Answer:
a) 28
Step-by-step explanation:
Given information,
→ w = 5
→ x = 9
→ y = 2
The given expression is,
→ x + 20 - 1
Let's solve the expression,
→ x + 20 - 1
→ 9 + 20 - 1
→ 29 - 1
→ 28
Hence, the answer is 28.
Two sides of a triangle measure 8 and 13. what represents x, the possible length in inches of the remaining side
Answers
Answer:
the possible number would be 159 in
Step-by-step explanation:
5÷5
A.5.1.5
B. 5 (obviously wrong so please ignore this)
c.25
D. 1
E. 75
Answers
Answer:1
Step-by-step explanation: so bro if yo do 5*1/25 u can see
5 divided by 5 would be 1
Question 10 of 10
Which would not be a step in solving 5x + 15 + 2x = 24 + 4X?
A. Collect variable terms on one side.
OB. Isolate the variable.
C. Use the distributive property.
Ο Ο
D. Collect like terms.
SUBMIT
Answers
Answer:
first you correct like terns
1. -10(-0.32 - 0.2)
Plz help
Answers
Answer:
5.2 would be the answer
Tina has volunteered at the pet shelter 4 more times than Kai. Tina has volunteered 16
times Which equation represents this situation?
A. 16+k-4
B. 16k-4
C. K+4=16
D. 4K=16
Answers
The correct answer is option C: \(\(k + 4 = 16\).\) This linear equation represents the relationship between Tina and Kai's volunteer times.
To represent the given situation, the equation that correctly represents the relationship between Tina's volunteer times (Tina = 16) and Kai's volunteer times (Kai = k) is:
\(\[Tina = Kai + 4\]\)
In this equation, Tina's volunteer times are represented by "Tina," and Kai's volunteer times are represented by "Kai." Since Tina has volunteered 4 more times than Kai, we add 4 to Kai's volunteer times to get the total number of times Tina has volunteered.
Substituting the given values, we have:
\(\[16 = k + 4\]\)
This equation represents the fact that Tina has volunteered \(16\) times, which is equal to Kai's volunteer times (k) plus the additional 4 times that Tina volunteered.
Simplifying the equation:
\(\[k + 4 = 16\]\)
This equation is equivalent to the original equation and represents the relationship between Tina and Kai's volunteer times. Hence, the correct answer is option C: \(\(k + 4 = 16\).\)
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Lynn paid $12.21 for ribbon. The cost per yard was $1.48.
How many yards of ribbon did Lynn buy?
Answers
Answer:
$12.21 / 1.48 = 8.25
Step-by-step explanation:
The girls in Lana’s troop set a goal to sell 1,000 boxes of cookies this year. There are 13 girls in the troop. At least how many boxes of cookies should each girl sell to reach their goal?
Answers
Answer:
This question would be answered by doing devision because you are splitting the amount of cookies that should be delivered amongst 13 girls.
1,000/13
76.92307692
That is what came out in my calculator. I don't know if you need it in decimal or in a solid integer but if you were to round 76.9 you would get 77, it is always good to check your work so,
77 times 13
1001
That equals 1001 so that would help at least reach their goal of 1,000 boxes of cookies.
Step-by-step explanation:
I really hope this helps!
Carly, an office manager, needs to find a courier to deliver a package. The first courier she is
considering charges a fee of $13 plus $3 per kilogram. The second charges $5 plus $4 per
kilogram. Carly determines that, given her package's weight, the two courier services are
equivalent in terms of cost. What is the weight? How much will it cost?
At a package weight of
kilograms, the two couriers both cost $
Answers
Answer:
At a package weight of 8 kilograms, the two couriers both cost $37
Step-by-step explanation:
Let's say the package weighs w kg.
First courier: 13 + 3 per kg = 13 + 3 for each w = 13 + 3w
Second courier: 5 + 4w
They are equal in cost, so
13 + 3w = 5 + 4w
subtract 3w from both sides to put all the variables on one isde
13 = 5 + w
subtract 8 from both sides to solve for w
w = 8
plug w=8 into one side of the original equation to solve for cost
13 + 3w = 5 + 4w = 37
12m = 84.72
I’m confused
Answers
Simplifying
12m = 84.72
Solving
12m = 84.72
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Divide each side by '12'.
m = 7.06
Simplifying
m = 7.06
Do you know what the sales tax is in your state?
Answers
Answer:
no ;)
Step-by-step explanation:
what is the median of the data set represented by the box plot shown below? 38,45,50,60,75
Answers
Answer:
50
Step-by-step explanation: