Concerns about the climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g. from renewable sources) and petrodiesel (from fossil fuel). Random samples of 34 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?
Answers
Answer:
a) 99% of the sample means will fall between 0.933 and 0.941.
b) By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?
Samples of 34 means that \(n = 34\)
We have that \(\mu = 0.937, \sigma = 0.009\)
By the Central Limit Theorem, \(s = \frac{0.009}{\sqrt{34}} = 0.0015\)
Within what interval will 99% of the sample means fail?
Between the (100-99)/2 = 0.5th percentile and the (100+99)/2 = 99.5th percentile.
0.5th percentile:
X when Z has a pvalue of 0.005. So X when Z = -2.575.
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(-2.575 = \frac{X - 0.937}{0.0015}\)
\(X - 0.937 = -2.575*0.0015\)
\(X = 0.933\)
99.5th percentile:
X when Z has a pvalue of 0.995. So X when Z = 2.575.
\(Z = \frac{X - \mu}{s}\)
\(2.575 = \frac{X - 0.937}{0.0015}\)
\(X - 0.937 = 2.575*0.0015\)
\(X = 0.941\)
99% of the sample means will fall between 0.933 and 0.941.
(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?
By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.
Related Questions
Math! Who’s knows the answer?
Answers
Answer:
M=30 degrees
because 102+148=150 and 180-150=30. (remember the sum of a triangle is 180 degrees)
the congruence statement would be SAS (side angle side) because 102 and 48 are the same in both triangles, but the third side is not the same.
will mark brainleist pls help
Answers
Answer:
x = 31°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , that is
x + 54° + 95° = 180°
x + 149° = 180° ( subtract 149° from both sides )
x = 31°
Describe the graph that would be used to solve the equation -x^2+4=x+2 using a system of equations. How will you use the graph to find the solution(s)?
Answers
The solution of the equation -x² + 4 = x + 2 is at x = -2 and x = 1
What is an equation?An equation is an expression that shows how numbers and variables are related to each other.
Given the quadratic equation:
-x² + 4 = x + 2
Collecting like terms:
x² + x - 2 = 0
Plotting using a graph; the solution of the equation can be gotten by getting the point the graph crosses the x axis.
The solution is at x = -2 and x = 1
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k) -3 x 9 = -27
l) 4 x (-6) = -24
m) 6 x 7 = 42
n) -7 x 8 = -56
o) -13 x -9 = 117
p) 9 -3 = -3
q) -24 6 = -4
r) -56 -8 = 7
s) 26 -5 = -5.2
t) -64 7 = -9.14
are these correct?
Answers
The expressions k to t are evaluated correctly
How to determine if the expressions are correctFrom the question, we have the following parameters that can be used in our computation:
The expressions k to t
To determine if the expressions are correct, we evaluate each expression and state if it is correct or not
Using the above as a guide, we have the following:
k) -3 x 9 = -27: Yes, this is correct.l) 4 x (-6) = -24: Yes, this is correct.m) 6 x 7 = 42: Yes, this is correct.n) -7 x 8 = -56: Yes, this is correct.o) -13 x -9 = 117: Yes, this is correct.p) 9 / -3 = -3: Yes, this is correct.q) -24 / 6 = -4: Yes, this is correct.r) -56 / -8 = 7: Yes, this is correct.s) 26 / -5 = -5.2: Yes, this is correct.j) -64 / 7 = -9.14 This is correct when approximatedRead more about expressions at
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As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answers
Answer:
154.2
Step-by-step explanation:
To find the average of the bowlers scores, you have to find the mean by adding the values and dividing by the number of values.
To find the bowlers average add the scores and divide by the number of games.
143+156+172+133+167/5=154.2 is the average score for the bowler.
What do I do?
Brief Calculus Question: Find Each limit (if it exist)
Answers
For the given function the value of limits are
\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\) is 5
\(\lim _{x\to 0^+}\left(f\left(x\right)\right)\) is 0
\(\lim _{x\to 0}\left x^2+5\)is 5
The given function is f(x)= x²+5, when x≤0
f(x)=2x when x>0
\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\)
Which is \(\lim _{x\to 0^-}\left x^2+5\)
The given limit is a left hand limit as there is minus in the limits
When we apply x as 0 we get the value 5
Now \(\lim _{x\to 0^+}\left(f\left(x\right)\right)\)
So \(\lim _{x\to 0^+}\left 2x\)
The given limit is a right hand limit as there is positive in the limits
When we apply x as 0 we get 0
Now \(\lim _{x\to 0}\left(f\left(x\right)\right)\)
Which is \(\lim _{x\to 0}\left x^2+5\)
We get 5
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A straw is placed inside a rectangular box that is 3 inches by 2 inches by 9 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Answers
The diagonal of the rectangular box will be 9.7 inches.
Given that:
Length, L = 3 inches
Width, W = 2 inches
Height, H = 9 inches
The diagonal of the rectangular prism is given as,
d² = L² + W² + H²
The diagonal of the rectangular box will be calculated as,
d² = 3² + 2² + 9²
d² = 9 + 4 + 81
d² = 94
d = √94
d = 9.7 inches
The diagonal of the rectangular box will be 9.7 inches.
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what is 258 divided by 4?
Answers
The quotient of 258 divided by 4 is calculated to be 64.5
Division is considered to be one of the four basic operations of arithmetic. The other three are multiplication, addition, and subtraction, and they can be defined as how numbers are combined to make new numbers.
Out of the four basic operations, division is the process of splitting an amount or a number into equal parts.
In division, the numerator is the top number of a fraction, and on the other hand, the denominator is the bottom number of a fraction and the result of division is called the quotient
In this case, 258 is the numerator and 4 is the denominator;
258 / 4 = 64.5
Therefore the quotient of this division is calculated to be 64.5
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Solve the problem.
A person is watching a boat from the top of a lighthouse. The angle of depression from the person to the boat is
28° . The lighthouse is 200 feet tall. How far away is the boat? Round to the nearest foot.
Answers
Tan 28= 200/x
x=200/ tan 28
x=376.14
x=376
Step-by-step explanation:
Hope this helps!
The boat is x=376 foot away from the light house.
A person is watching a boat from the top of a lighthouse. The angle of depression from the person to the boat is 28°. The lighthouse is 200 feet tall.
Trigonometry is defined as the study of angles.
Let the boat is x distance away from the lighthouse
assume a right-angle triangle ABC with AB =perpendicular=200, BC = base=X, Angle CAB = 28°(angle of depression means the angle from the boat to the top of lighthouse is also 28°)
tan28 = 200/X
X = 200/tan28
X = 376 foots
Thus, The boat is x=376 foot away from the lighthouse.
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Find the measure of the indicated angle.
99⁰
96⁰
98⁰
92°
L
120°
K
N
M
64
Answers
Answer:
? = 92°
Step-by-step explanation:
the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°
How do you simplify (2/3) with a sqrt of 2
Answers
Select the correct answer.
Which expression is equivalent to sin (2x) cos x?
Answers
The equivalent trigonometric expression to sin(2x)cos(x) is given as follows:
sin(2x)cos(x) = 2sin(x)cos²(x).
How to obtain the equivalent trigonometric expression?The expression for this problem is defined as follows:
sin(2x)cos(x).
The trigonometric identity used to simplify sin(2x) is given as follows:
sin(2x) = 2sin(x)cos(x).
Hence the expression can be written as follows:
sin(2x)cos(x) = 2sin(x)cos(x)cos(x)
sin(2x)cos(x) = 2sin(x)cos²(x).
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fill in the mission numbers to make the fractions equivalent. 1/2 and /8= 4/12 and /60= 2/3 and /12= 4/4 and /8=
Answers
To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:
1/2 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
1/2 and 4/8
Now, the fractions are equivalent.
---
4/12 and __/60
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:
4/12 and 20/60
Now, the fractions are equivalent.
---
2/3 and __/12
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
2/3 and 8/12
Now, the fractions are equivalent.
---
4/4 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:
4/4 and 8/8
Now, the fractions are equivalent.
ksjdfnsdjkfnskfjsndjkfsndjkf
Answers
Natural logs can be written as _______.
Answers
Answer:
Step-by-step explanation:
The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.
Answer:
Ln x as opposed to log x
Step-by-step explanation:
Write as a fraction
3÷151
Answers
Answer:
3/151
Step-by-step explanation:
That's the answer
Lynn is making custom bricks. She combines 39 pounds of water and 48 pounds of brick dust
in a mixing bucket. She spills 13 pounds of the mixture while stirring the contents. The
mixture is then poured into small dirt holes to make bricks. Each brick requires 7 pounds of
mixture, and the leftover mixture is washed out of the mixing bucket
What is the greatest number of bricks Lynn can make?
bricks
How many pounds of mixture will be washed out of the bucket if Lynn makes the greatest
number of bricks?
pounds
Answers
Greatest number of bricks Lynn can make is 10 and 4 pounds of the mixture will be washed out of the bucket
Pounds of water = 39
Pounds of brick dust = 48
Total mixture = 87 pounds
Mixture spilled = 13 pounds
Mixture remaining = 87 pounds - 13 pounds
= 74 pounds
Mixture in each brick holes = 7 pounds of mixture
Greatest number of bricks Lynn can make = Mixture remaining ÷ Mixture in each brick holes
= 74 pounds ÷ 7 pounds
= 10 remaining 4 pounds
Therefore,
Greatest number of bricks Lynn can make is 10 and 4 pounds of the mixture will be washed out of the bucket
https://brainly.com/question/16718414
Answer: Greatest number lynn can make is 10 Bricks.
4 pounds will be washed out the bucket.
Step-by-step explanation:
Answer and I will give you brainiliest
Answers
Answer:
d=1.3t
Step-by-step explanation:
In the equation,
Distance = 1.3 times time (in seconds.)
Answer:
6.5
Step-by-step explanation:
1.3x5=6.5
brwainliest plz
HELPPPPPPPPPPP. please explain how u got the answer
Answers
Step-by-step explanation:
the key is x = 0.
also I see in the first table no "run-away" effect of some values, so my first suspicion is : it is linear.
let's test it.
a linear function is a line :
y = ax + b
remember, x = 0 is a key element.
y = a×0 + b
-3 = a×0 + b
-3 = b
so, we know, the line function is
y = ax - 3
now, for the a. let's use the next xy pair (1, 1).
1 = a×1 - 3
4 = a
aha ! our line function is therefore
y = 4x - 3
verify with the next 2 points (2, 5) and (3, 9)
5 = 4×2 - 3 = 5 correct
9 = 4×3 - 3 = 9 correct
linear type and equation confirmed.
the second table :
yes, we see relatively big y values compared to the x values.
and the y values follow the powers of 2
so it seems to to be exponential.
64 = 2⁶
32 = 2⁵
16 = 2⁴
8 = 2³
so, while x increases, the powers of 2 decrease. so, we must build something like y = 2^x, but it must run contrary to the increase in x.
the old trick : c-x.
again, x= 0 is key. when x = 0 we get the biggest y (64). that means that gives us c.
64 = 2^(c-x) = 2^(c-0) = 2^c = 2⁶
=> c = 6
so, we suspect the exponential function
y = 2^(6-x)
let's verify with the other points
(1, 32)
32 = 2^(6-1) = 2^(5) = 32 correct
(2, 16)
16 = 2^(6-2) = 2^(4) = 16 correct
(3, 8)
8 = 2^(6-3) = 2^(3) = 8 correct
so, yes, it is the exponential function
y = 2^(6-x)
what was the key to getting support for converting from petroleum to synthetic lubricants?
Answers
Answer:
Step-by-step explanation:
please help 3/4 divided by 1/8
Answers
Answer:
6
Step-by-step explanation:
please help 3/4 divided by 1/8
3/4 : 1/8 =
3/4 x 8 =
24/4 =
6
40% of the cost was tax. if the taxes paid were $15,000, what was the total cost of the car?
Answers
Answer:
$37500
Step-by-step explanation:
For this we can simply create a proportion of the percentages.
.4 / 1 == 15000 / x
Now we solve for x:
x = 15000/.4
x = 37500
Thus, the cost of the car was $37,500.
Cheers.
Write the numbers associated with the points that are
graphed on the complex plane.
Z1 =. + Oi
Z2 = 0 - I
Z3 =. +i
Answers
The complex numbers graphed on the plane are given as follows:
z1 = 3 + 0i.z2 = 0 - 2i.z3 = -2 + i.What are complex numbers?Complex numbers are number that are divided into a real part and an imaginary part, according to the definition given as follows:
z = a + bi.
In which:
a is the real part.b is the imaginary part.On the complex plane, we have that:
The horizontal axis represents the real part of the number.The vertical axis represents the imaginary prat of the number.As the number z1 has a horizontal coordinate of 3 and a vertical coordinate of 0, it is given as follows:
z1 = 3 + 0i.
As the number z2 has a horizontal coordinate of 0 and a vertical coordinate of -2, it is given as follows:
z2 = 0 - 2i.
As the number z3 has a horizontal coordinate of -2 and a vertical coordinate of 1, it is given as follows:
z3 = -2 + i.
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A researcher collected data from car shoppers about their favorite car color. He asked 250 people about their favorite vehicle color. How many more people said their favorite color is white compared to those who said black. Your answer should be written as a number not a percentage. And then the percents for the circle graph are 20% red 24% white 32% blue 18% black 4% silver and 2% other
Answers
Answer:
35 more preferred white
Step-by-step explanation:
Black 18% * 250 = 18/100 * 250 = 45
White 32%*250 = 32/100 * 250 = 80
The difference is 80 - 45 = 35
If lia has 1,00000$ and she spend 2,000 on her nails and feet to get done then.She buys new chanel shoes that cost 1,000 and then buys 400$ worth of clothes how much money will be left? Pls help
Answers
And it’s 100,000 not 1,00000
Answer:she will have 96,600
Step-by-step explanation:
Hope this helps
Mrs. Drew wants to build a square sandbox with an area of 256 square feet. What is the total length of wood Mrs. Drew needs to make the sides of the sandbox?
Answers
Answer:
64 ft
Step-by-step explanation:
square root of 256 is 16. so each side is 16 ft. 16*4=64
The total length of wood is 16 feet
What is area of square?Area of a Square = Side × Side.
Therefore, the area of square = Side2 square units.
Given:
Area of square = 256 square feet
Now,
Area of square = 4*side
256 = side * side
side ²= 256
side = √256
side =16
Hence, the length of wood is 16 feet.
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What is the value of N
N=5
Answers
Answer:
5
Step-by-step explanation:
If N=5 the value of N is 5. You said it : )
Answer: 5
If I Helped, Please Mark Me As Brainliest, Have A Great Day :D
H
6:00 PM
What is a frostbite?
Answers
This is the question I need an answer to
Answers
The correct option is (D) The subject would not receive treatment and could spread the disease.
The probability is 0.04
and, The unfavorable consequence of error is "The subject would not receive treatment and could spread the disease."
What is Probability ?In mathematics, probability defines the occurrence of something. Or we can say that it defines the chance of something to be happen or occur.
Probability is the mathematical branch that studies and deal with the possible outcomes of some given events together or some set of event with the outcomes of distributions.
The minimum value of probability is 0 while the maximum value is 1 .
How to calculate probability?Suppose if there are some favorable outcomes whose probability we have to find out then the formula is :
\(prob ( fav \ outcome) = \frac{number \ of \ favorable \ outcome}{total \ number \ of \ outcomes}\)
In the given question :
total outcomes = 333 + 14 = 347
favorable outcome = 14
thus, probability = 14 / 347 = 0.04
and unfavorable consequence of error is "The subject would not receive treatment and could spread the disease."
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Pls I need help
Given h(x) = -2x + 4, solve for a when h(2)
= -
- 8.
Answers
Answer:
x = 6
Step-by-step explanation:
