Answer:
The margin of error is of 623.2016.
The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem, and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. The population standard deviation for Compound 1 is 4414 miles.
This means that [tex]\mu_1 = 37866, s_1 = \frac{4414}{\sqrt{243}} = 283.16[/tex]
A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. The population standard deviation for Compound 2 is 2368 miles.
This means that [tex]\mu_2 = 45789, s_2 = \frac{2368}{\sqrt{268}} = 144.65[/tex]
Distribution of the difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
The mean is:
[tex]\mu = \mu_1 - \mu_2 = 37866 - 45789 = -7923[/tex]
The standard deviation is:
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{283.16^2 + 144.64^2} = 317.96[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.96*317.96 = 623.2016[/tex]
The margin of error is of 623.2016.
The lower end of the interval is the sample mean subtracted by M. So it is -7923 - 623.2016 = -8546.2016
The upper end of the interval is the sample mean added to M. So it is -7923 + 623.2016 = -7299.7984
The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).
Helpppppppppppppppppppppppppppppppppppp
try this one method. I hope it will help a little
Which side lengths form a right triangle?
Answer:
Answer:[tex] \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ [/tex] Pythagoras law:h²=p²+b²
needed to apply
4²+8²=12²
80≠144 not a right angled triangle
again
2²+√5²=3²
9=9/
side are a right angled triangle
again
2²+2²=(√8)²
4+4=8
8=8
side are a right angled triangle
y=x-3
y+3x=1 solve by substitution
Answer:
x = 1
Step-by-step explanation:
x - 3 + 3x = 1
4x - 3 = 1
4x = 4
x = 1
Answer:
x=1, y=-2
Step-by-step explanation:
According to the substitution property, if x = y, then x can be substituted for y in any equation, and y can be substituted for x in any equation.
We are already given the values:
y=x-3
y+3x=1
We can substitute y into the equation.
As so-
[tex]x-3+3x=1[/tex]
Combine common terms:
[tex]4x-3=1[/tex]
Now solve for x. To solve for a variable, we must isolate it:
Add 3 to both sides:
[tex]4x=4[/tex]
The last thing, 4 is being multiplied to x, so we must divide it to both sides to isolate the variable.
[tex]x=1[/tex]
Now we can just substitute the x value into the y equation:
[tex]y=x-3\\y=1-3\\y=-2[/tex]
It is always better to check our answers, we can substitute our x and y into the equation:
[tex]-2+3(1)=1\\-2+3=1\\1=1[/tex]
We are right! :)) Hope it helps!
x=1, y=-2
(1,-2)
Please help me I'm so bad at math and doing AFDA really doesn't help..
place for the solution with quadratic equation
Answer:
4, 16, -4, 2, -1
x = 4±√(16-4(2)(-1)/4
Correct expression:
Step-by-step explanation:
Given the expression
2x² - 8x - 7 = -4x - 6
Rewrite in standard form
2x² - 8x + 4x - 7 + 6 = 0
2x² - 4x - 1 = 0
Get the coefficients
Given the standard form ax^2 + bx + c = 0
ax^2 = 2x^2
a = 2
bx = -4x
b = -4
c = -1
Use the general formula to find the factors
x = -b±√b²-4ac/2a
Substitute the coefficients
x = -(-4)±√(-4)²-4(2)(-1)/2(2)
x = 4±√(16-4(2)(-1)/4
Hence the values are 4, 16, -4, 2, -1
please help me In exponents we have to write
Answer:
1. -3/13
2. (simplified) 8 / (exponential form) 2^3
3. 1265625/16384
4. 5
Step-by-step explanation:
no need for explanation just try the app Photo math (no space in the photo and math)
What is 11 3/6 rounded to the nearest
Answer:
12
Step-by-step explanation:
Plz help me with this two question
The results of a coin toss are shown.
What is P(heads)?
H T H H H T H T T H H T H T T T H H T H T T H H H H T H T T
A. 8/15. B.7/17. C.1/2. D3/5
Answer:
A is the answer!
Because that's reduced of 16/30
Can someone help me with this one?
Answer:
well I can see not see the graph so for this the + whatever is the y intercept which means when the line goes through the y axis and with the X find a point that is at the tip of a square then count up or down and if you count up and over it is positive and down and over it negative if i cann the graph I would love to help you.
Multi-Step Equations - PracticeCheck your SolutionCheck your SolutionCheck your SolutionCheck your SolutionCheck your Solution123456-3m - 5 = 5m - 136(y + 7) = 2(y - 3)3x + 2(x - 5) = 2510q + 3q + 5 = 2(q - 3)(x + 6) = 1323(x - 9)
Answer:
i don't get what i should do its all messed up
Step-by-step explanation:
Tina owns a house that is worth
$ 125,000, a car that is worth $4,000
and miscellaneous items worth
$3,200. She also has $5,000 in
student loans and $572 in credit card
debt. How much is Tina's net Worth?
Answer:
126,628
Step-by-step explanation:
125,000+4,000+3,200-5,000-572
Net worth is your dollar amount in assets minus liabilities, so debts and loans, in total the net worth is $126,628
Will give brainliest if anyone answers this one
LOCKER NUMBERS What is the probability that a 6-digit locker combination with the digits 3, 5, 7, 3, 5, and 2 is the number 53-27-35?
A.1/90
B.1/180
C.1/720
D.1/360
Find the distance between -4 and 6 on the number line .
Answer:
10
Step-by-step explanation:
The formula for finding distance between 2 points on a number-line is absolute value. We need to find the absolute value of -4+6. |-4| + |6| = 10
Absolute Value negates any negatives.
An employee put $10,000 in a retirement
account that offers 4% interest
compounded annually.
The employee makes no additional deposits or
withdrawals. Which amount is closest to the interest
the employee will have earned at the end of 12 years?
A) $4,520.14
B) $5,200.36
C) $6,010.32
D) $7,340.18
PLS ANSWER ASSP WILL GIVE BRAINLIEST ANSWER
C. $6010, I plugged the information into a simple compound interest calculator.
Dan wants to buy carpet. To cover his hole living room, except for the tiled floor. The tiled floor is 4 5/6 ft by 2 1/3. Find the area the carpet needs to cover
Answer:
11.2777778 feet (11 feet 321⁄64 inches)
Step-by-step explanation:
Answer:
11 27/100
Step-by-step explanation:
L (length) times W (width) = A (area)
On an
Air Indian flight there are
9 boys, 5 Indian Children, 0
9 men, 7 foreign boys 14 Indian, 6 indian male
and 7 foreign female. What is the
number of people on board the plane.
Answer:
43
Step-by-step explanation:
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The people at the Cloak soft drink company believe that their brand of drink is favored over their competitor's brand, Pempsi, by the majority of people. A quick survey is conducted to test this belief. Forty people are asked whether they prefer Cloak or Pempsi, and 28 people did prefer Cloak. A statistician at Cloak wishes to construct a 95% confidence interval for the proportion of people that prefer Cloak soft drink. Drag the blue marker from above the words 'lower bound' to the lower bound of the confidence interval on the number line provided. Drag the red marker from above the words 'upper bound' to the upper bound of the confidence interval on the number line provided.
Solution :
[tex]$p = \frac{28}{30}$[/tex]
= 0.93
Given :
[tex]$a=0.05$[/tex]
[tex]$z(0.025)=$[/tex] [tex]$1.96$[/tex] (from standard normal table)
So the lower bound is
[tex]$=p+z\times \sqrt{p \times \frac{1-p}{n}}$[/tex]
[tex]$=0.7+0.93\times \sqrt{0.7 \times \frac{1-0.7}{30}}$[/tex]
= 1.63 + 0.083
[tex]$=1.73$[/tex]
HELP WILL GIVE BRANLIEST
Calculate the area of the following image:
11.1.21 A survey asked, "How many tattoos do you currently have on your body?" Of the males surveyed, responded that they had at least one tattoo. Of the females surveyed, responded that they had at least one tattoo. Construct a % confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval. Let represent the proportion of males with tattoos and represent the proportion of females with tattoos. Find the % confidence interval for . The lower bound is nothing. The upper bound is nothing. (Round to three decimal places as needed.)
Complete question :
The Harris Poll conducted a survey in which they asked, "How many tattoos do you currently have on your body?" Of the 1205 males surveyed, 181 responded that they had at least one tattoo. Of the 1097 females surveyed, 143 responded that they had at least one tattoo. Construct a 95% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.
Answer:
(−0.0085 ; 0.0481)
Step-by-step explanation:
Given that :
n1 = 1205 ; x1 = 181 ; n2 = 1097 ; x2 = 143 ; α = 95%
Zα/2 = 1.96 ( Z table)
Confidence interval : (p1 - p2) ± E
E =Zα/2 * √[(p1q1/n1) + (p2q2/n2)]
p1 = x1 /n1 =181/1205 = 0.1502
q1 = 1 - p1 = 1 -0.1502 = 0.8498
p2 = x2/n2 = 143/1097 = 0.1304
q2 = 1 - p2 = 1 -0.1304 = 0.8696
E = 1.96 * √(0.0001059 + 0.0001033)
E = 0.0283
p1 - p2 = 0.1502 - 0.1304 = 0.0198
Lower boundary = 0.0198 - 0.0283 = −0.0085
Upper boundary = 0.0198 + 0.0283 = 0.0481
(−0.0085 ; 0.0481)
Does the equation below represent a
direct proportion? If yes, identify
the constant of proportionality.
х = 6у
A. No
B. Yes, 36
C. Yes, -6
D. Yes, 1/6
Step-by-step explanation:
The given equation is :
x = 6y ...(1)
Here,
x and y are variables and 6 is a constant number
It means,
x and y are related directly to each other i.e.
x ∝ y
or
x = ky .....(2)
Comparing equation (1) and (2)
k = 6
Hence, yes they are in direct proportion and the value of constant of proportionality is 6.
Answer:
yes / 1/6
Step-by-step explanation:
I’ll give points + brainalist for the correct answer (:
Answer:
x=18
Step-by-step explanation:
since they are vertical angle they are the same so since its 2x divide 36/2=18
Answer:
x=18
Step-by-step explanation:
[tex]2x = 36 \\ x = \frac{36}{2} \\ x = 18[/tex]
A plataform is made of two rectangular prisms
Answer:
12 cubic meters
Step-by-step explanation:
Large - 4x3x2=24
Small - 2x3x2=12
24-12=12
graph x + 4= -8(y-2)^2
Answer:
It should be B!
Step-by-step explanation:
The graph looks small and on the left second quadrant
Answer:
Its b
Step-by-step explanation:
Just got it right on edge
. El siguiente cuadro muestra el porcentaje de votación que alcanzaron los
cuatro partidos en las últimas elecciones para alcaldes provinciales, en una
provincia en la que votaron 65 000 electores.
Partido %
Progreso posible 42%
Bienestar para todos 28%
Todos unidos 16%
Camino al éxito 12%
Votos nulos o en blanco 2%
¿Cuántos votos más debió obtener el candidato del partido “Bienestar para
todos” para igualar al candidato del partido “Progreso posible”?
a) 14
b) 9 100
c) 27 300
Answer:
Can you translate?
Step-by-step explanation:
To english..?
What is the balance for B?
DEPOSITS WITHDRAWALS
BALANCE
$565.00
$50,00
А
DATE DESCRIPTION OF TRANSACTION
7/1
7/5
Babyutting
717
Birthday money
7/12
Cell phone bi
7/15
Car Insurance
$95.00
В
$39.20
С
$45.20
D
Lunch with friends
$15.70
E
7/18
7/19
Babysitting
$60.00
F
O 609.90
O 615.00
O 625.60
Ооооо
O 669.90
670,80
O 710.00
1 point
What is the balance for C?
Can somebody give me the answer to this question please
Answer:
B
Step-by-step explanation:
Football has the highest number of votes in the chart.
What shape are the faces, other than the base,
of a pyramid?
Answer:
A triangle
Step-by-step explanation:
Need the answer. Pic to describe.
Answer:
Step-by-step explanation:
Can someone seriously help me!!!!!
Answer:
Step-by-step explanation:
This should help I hope