Suppose you compile all possible samples of 25 children of preschool age in your school district. If you calculate the mean of each sample (M) and create a frequency distribution of these means, this distribution is referred to as the .
Answers
The distribution of means of all possible samples is referred to as the sampling distribution of the mean.
The sampling distribution of the mean refers to the distribution of sample means that would be obtained .
If we were to take all possible samples of a certain size from a population.
Here, considering all possible samples of 25 children of preschool age in your school district.
The key concept is that the sample means will vary from one sample to another, even if they are drawn from the same population.
However, as the sample size increases, the sampling distribution of the mean tends to become more concentrated around the population mean.
The central limit theorem states that,
The sampling distribution of the mean will be approximately normally distributed, regardless of the shape of the population distribution.
This holds true for large enough sample sizes typically around 30 or more or when the population distribution is approximately normal.
The mean of sampling distribution of mean will be equal to population mean, which provides an unbiased estimate of the population mean.
The standard deviation of the sampling distribution of the mean, often referred to as the standard error,
Calculated by dividing the population standard deviation by the square root of the sample size.
By creating a frequency distribution of these sample means, observe pattern of variation and spread of means around population mean.
Sampling distribution allows us to make inferences and draw conclusions about the population based on the sample data.
Therefore, sampling distribution of mean is distribution of sample means obtained from all possible samples of a specific size drawn from a population.
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Related Questions
Help this girl out. This maths is killing me
Answers
Answer:
x=49
y=63
Step-by-step explanation:
Answer:
x=49
y=63
Step-by-step explanation:
The fifth graders were given sandwiches for lunch during their field trip. Nathan ate 5/6 of his sandwich, Leroy ate 7/8 of his sandwich, and Sofia ate 5/8 of her sandwich. Who ate the greatest amount of their sandwich?
Answers
Answer:
Leroy ate the most
Step-by-step explanation:
(a)
What is the missing number in the box?
3.33 X
= 55.5 x 38
help me pls
Answers
Answer:
(this is the equation I perceived from your information, if it's not correct make sure to notify me in the comment section below)
3.33x = 55.5*38
Simplify;
3.33x = 2109
Isolate 'x' by applying inverse operations,
The inverse operation of multiplication is division because 3.33 is being multiplied by 'x'.
÷3.33 ÷3.33
x = 633.333..
Answer:
633.333333
Step-by-step explanation:
3.33 x (blank) = 55.5 x 38
55.5 x 38 = 2109
2109 / 3.33 = 633.333333
3.33 x 633.333333 = 55.5 x 38
Hope this helped. If you need further explanation, let me know!
- profparis
An automatic filling machine is used to fill 2-litre bottles of cola. The machine’s output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of 0.01 litres. Output is monitored using means of samples of 5 observations.
Determine the upper and lower control limits that will include roughly 95.5 percent of the sample means.
If the means for 6 samples are 2.005, 2.001, 1.998, 2.002, 1.995 and 1.999, is the process in control?
Answers
The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.
Now let's check if the process is in control using the given sample means:
To determine the upper and lower control limits for the sample means, we can use the formula:
Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))
Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))
In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.
For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.
Given:
Mean = 2.0 litres
Standard Deviation = 0.01 litres
Sample size (n) = 5
Using the formula, we can calculate the upper and lower control limits:
UCL = 2.0 + (1.96 * 0.01 / sqrt(5))
LCL = 2.0 - (1.96 * 0.01 / sqrt(5))
Calculating the values:
UCL ≈ 2.0018 litres
LCL ≈ 1.9982 litres
Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.
Now let's check if the process is in control using the given sample means:
Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997
Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.
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What is the distance between -10 and 9?
1.-8
2.-14
3.-19
4.-15
Answers
A car used 1/64 of a gallon of gas to drive 1/4 of a mile. At this rate, how many miles can a car travel using 1 gallon of gas?
Answers
Answer:
16 miles
Step-by-step explanation:
In order to find one gallon of gas, you multiply the 64 by 1/64 which will get you to 1 whole. Now you multiply the 64 by the 1/4 miles which will give you 16 miles.
18
Jerry says that a pencil is 2.4 inches long. If the pencil is actually 3.6 inches long, what was jerry's percent
error?
30%
33%
36%
39%
Answers
Answer:
Step-by-step explanation:
he's off by 1.2 sooo
divide 1.2 / 3.6 = 0.3333333333333
or 33% approx.
Which of the following graphs model exponential functions? Select all that apply.
Answers
The graphs model exponential functions will remain positive. Then the correct options are A and D.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor. The exponent is given as
y = a(b)ˣ
If the initial value a is positive and x is positive, then the graph of the exponent function will approach infinity as x increases.
If the initial value a is positive and x is negative, then the graph of the exponent function will approach zero as x increases.
The graphs model exponential functions will remain positive.
Then the correct options are A and D.
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what is equivalent to 4/-3
Answers
Answer:
86 is equivalent to 43 because 8 x 3 = 6 x 4 = 24. 129 is equivalent to 43 because 12 x 3 = 9 x 4 = 36.
if a > b, under what condition is | - | = a - b?
Answers
If a > b, then |a - b| = a - b if a - b is positive. This means that the distance from a - b to zero on the number line is equal to a - b itself. If a - b is negative, then |a - b| is equal to the opposite of a - b.
The absolute value of a - b is equal to a - b if a - b is positive because the absolute value of a number is the distance from that number to zero on the number line. So, if a is greater than b, then a - b is a positive number. Therefore, the distance from a - b to zero on the number line is equal to a - b.
The absolute value of a number is the distance from that number to zero on the number line. For example, the absolute value of 5 is 5 because the distance from 5 to 0 on the number line is 5 units. The absolute value of -5 is also 5 because the distance from -5 to 0 on the number line is also 5 units.
Now, let's look at the expression |a - b|. This means the absolute value of the difference between a and b. If a is greater than b, then a - b is a positive number. For example, if a = 10 and b = 5, then a - b = 5. So, |a - b| = |10 - 5| = |5| = 5.
However, we are looking for the condition under which |a - b| = a - b. This means that the absolute value of a - b is equal to a - b itself. This only happens when a - b is positive. Let's use the same example as before. If a = 10 and b = 5, then a - b = 5. In this case, a - b is positive, so |a - b| = |10 - 5| = |5| = 5, which is equal to a - b.
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Before starting a game, Salmiah and Devi has a total of 30 marbles, Then, each of them lost 6 marbles at the end of the game. The product of the number of their marbles at the end of the game was 80. Calculate the number of Salmiah's marbles and the number of Devi's marbles at the beginning of the game.
Answers
The number of Salmiah's marbles and the number of Devi's marbles at the beginning of the game are determined using mathematical operations as follows:
Salmiah = 14Devi = 16.How are the numbers determined?To determine the numbers, we use mathematical operations, including multiplication, subtraction, and addition.
The total number of lost marbles is determined as 12 by multiplying 6 by 2.
The difference between the beginning number of marbles and the lost marbles is computed by subtraction.
From the ending factors whose product will be 80, we add 6 each to determine the beginning numbers of marbles.
The total number of marbles at the beginning of the game = 30
The number of marbles lost by each contestant = 6
The total number of lost marbles = 12 (6 x 2)
The remaining number of marbles after the game = 18 (30 -12)
The factors of 18 that will become a product of 80 are 8 and 10.
The beginning number of marbles held:
Salmiah = 14 (8 + 6)
Devi = 16 (10 + 6)
Total marbles = 30
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A jet travels 1731 miles against the wind in 3 hours and 2151 miles with the wind in the same amount of time. What is the rate of the jet in still air and what is the rate of the wind
Answers
Velocity of jet in still air is 647 miles per hour and velocity of wind is 70 miles per hour.
Given,
Jet's velocity against wind 1731 / 3 = 577 mile per hour
flying with wind it 2151 / 3 = 717 miles per hour.
Let the velocity of jet in still air be x miles per hour and velocity of wind be y miles per hour.
As such its velocity against wind is x−y and with wind is x+y and therefore
x−y=577;
x+y=717
Adding the two
2x = 1294
x = 647
y= 717 − 647
y = 70
Hence velocity of jet in still air is 647 miles per hour and velocity of wind is 70 miles per hour.
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Solve the exponential equation. 4x = 0.5 -2 -1 -1/2
Answers
Answer:
\(x=-1/2\)
Step-by-step explanation:
\(4^x=1/2\)
Make the bases 2 on both sides of the equation.
\(2^{2^x}=2^{-1}\)
Multiply the exponents.
\(2^{2x}=2^{-1}\)
Cancel the bases.
\(2x=-1\)
Divide 2 into both sides of the equation.
\(x=-1/2\)
Solve the inequality: x - 20 < 35
Answers
Step-by-step explanation:
Here,
x -20 < 35
or, X<35+20
•X<55
(s3-6s)+4t2 when s=5 and 3=t
Answers
Answer:
9
Step-by-step explanation:
(5)3-6(5)+4(3)2
(15-30)+4(3)2
-15+ 24
=9
The exterior angle at vertex C of triangle ABC is
112°. If the bisector of side AB intersects side AC at point Q and line segment BQ
is perpendicular to AC, find the measure of angle ABC
Answers
Step-by-step explanation:
We know that the exterior angle at vertex C is equal to the sum of the interior angles at vertices A and B that are not adjacent to C. Thus, we have:
∠ACB = ∠A + ∠B
Since ∠AQC is the angle bisector of ∠BAC, we have:
∠AQD = ∠CQB
Since BQ is perpendicular to AC, we have:
∠BQC = 90° - ∠QCB
Now, let x be the measure of angle ABC. Then we have:
∠A = 180° - ∠ACB - x
∠B = 180° - ∠ACB - (90° - ∠QCB)
Substituting the given values and simplifying, we get:
∠A = 68° - x
∠B = 22° + ∠QCB
Now, we use the fact that the angles in a triangle add up to 180°:
∠A + ∠B + ∠C = 180°
Substituting the above expressions and simplifying, we get:
68° - x + 22° + ∠QCB + 112° = 180°
Simplifying further, we get:
∠QCB + x = 22°
But we also know that ∠QCB + x is equal to ∠ABC. Thus, we have:
∠ABC = 22°
Therefore, the measure of angle ABC is 22 degrees.
HELPPP
Verify that csc theta cos theta tan theta=1
Answers
Answer:
See Explanation
Step-by-step explanation:
\( \csc \theta \: \cos \theta \: \tan \theta = 1 \\ \\ LHS = \csc \theta \: \cos \theta \: \tan \theta \: \\ \\ = \frac{1}{ \sin \theta} \: \times \cancel{ \cos \theta }\: \times \frac{ \sin \theta}{ \cancel{ \cos \theta }} \\ \\ = \frac{1}{ \cancel{ \sin \theta}} \: \times \cancel{ \sin \theta} \\ \\ = 1 \\ \\ = RHS \\ \\ hence \: proved\)
Answer:
a) Only the first one is an identity.
Step-by-step explanation:
1). 8 cos O tan O csc O = 8 simplifies to:
cos O tan O csc O = 1
cos O * (sin O / cos O) * (1 /sin O)
= cos O sin O / cos O sin O
= 1
So it is identity.
2) 13 sec^2 O/ cos^2 O - tan^2 O / cos^2O
= 13 sec^2 O - tan^2 O / cos^2 O
Now sec^2 O = 1 + tan^2 O, so we have:
(13( 1 + tan^2 O) - tan^2 O) / cos^2 O
= (12 tan^2 O + 13) / cos^2 O
This is not always = 2 so its not an identity.
Step-by-step explanation:
How many radians are in one circle?
What is the ratio of Radians to Degrees in one circle?
What is the simplified form of the above ratio?
What do you multiply degrees by to convert to radians, and why? What do you multiply radians by to convert to degrees, and why?
Answers
1. One circle contains 2π radians.
2. The simplified ratio of radians to degrees in one circle is π/180°.
3. To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π.
1. There are 2π radians in one circle. This can be calculated using the following formula:
radians = π * degrees / 180°
π is a mathematical constant that is approximately equal to 3.14159.
degrees is the angle measure in degrees.
180° is the number of degrees in a circle.
Substituting these values into the formula, we get:
radians = π * degrees / 180°
radians = π * 360° / 180°
radians = 2π
Therefore, there are 2π radians in one circle.
2. The ratio of radians to degrees in one circle is 2π/360°. This can be simplified to π/180°.
3. To convert from degrees to radians, you multiply by π/180°. This is because there are π radians in a circle, and there are 360° in a circle. For example, to convert 90° to radians, you would multiply 90° by π/180°, which gives you π/2 radians.
To convert from radians to degrees, you multiply by 180°/π. This is because there are 360° in a circle, and there are π radians in a circle. For example, to convert π/2 radians to degrees, you would multiply π/2 by 180°/π, which gives you 90°.
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Using a long rod that has length , you are going to lay out a square plot in which the length of each side is μ . Thus the area of the plot will be μ2. However, you do not know the value of μ, so you decide to make n independent measurements X1, X2, . . . , Xn of the length. Assume that each Xi has mean (unbiased measurements) μ and variance σ2.
Answers
Proved that X² is not an unbiased estimator for μ²
Given,
The length of the square plot = μ
The area of the square plot = μ²
You have to make the independent measurements X₁, X₂,.....Xₙ
Variance = σ²
a) We have to show that X² is not an unbiased estimator for μ²
Here,
E(X²) = V(X) + [E(X)]²
= σ²/n + μ² ≠ μ²
Then,
X² is not an unbiased estimator for μ²
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(11 – 9)' – 2 x 4=
Please help
Answers
Answer: 2 − 8x
Step-by-step explanation:
tickets for a play cost $ 7 for students and $ 10 for adults. on opening night, all 380 seats were filled, and box office revenue was $ 3290.00. how many adults attended at the play?
Answers
The total number of adults who attended the play are 210.
Here, we are given that tickets for a play cost $ 7 for students and $ 10 for adults.
Total number of seats = 380
Box office revenue on opening night = $ 3290
Let the number of adults be x
Then, the number of students will be = (380 - x)
thus, we can form the following equation-
10x + 7(380 - x) = 3290
10x + 2,660 - 7x = 3290
3x + 2,660 = 3290
3x = 3290 - 2660
3x = 630
x = 630/3
x = 210
Thus, the total number of adults who attended the play are 210.
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-1.14285714286 in simplest form
Answers
Answer: to the nearest tenth its -1.1
to the nearest hundredth its -1.14
to the nearest thousandth its -1.143
as a percentage its −114.28571428%
-1.1,-1.14,-1.143 is the simplest form of -1.14285714286 in nearest 1oth, 100th and 1000th respectively.
The digit in the smallest location is unaffected if it is less than 5 in number. Rounding down is the process of reducing a number to zero after a certain number of digits. The digit in the smallest location is added with +1 if it is bigger than or equal to 5.
-1.14285714286 is simplified by rounding off
1. It can be rounded to the nearest tenth as -1.1
2. It can be rounded to the nearest hundredth as -1.14
3. It can be rounded to the nearest thousand as -1.143
Thus, -1.1,-1.14,-1.143 is the simplest form of -1.14285714286
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1/2 of 8 1/8=________
Answers
Answer:
One half of 8 1/8 is 4 1/16
Explanation:
Half of 8 is 4, and since the denominator of the fraction is 8, you'd have to double up to 16, since that's how fractions work.
The school library has 286 books. If the school librarian buys 12 books eachmonth for five months, how many books will the library have in all?
Answers
OK SO this is my report card, not my final. I have 2 more coming out so all three add up to my final. how much would i need in my classes to have an average of 90 smt for my FINAL report card?? pls send help
Answers
Answer:
90 times 3 is 270
270- 71 ( the average grade you have now)= 199
the 2 more report card average grade has to add up to 199 for you to get a 90.
The annual rainfall in Albany i. 33 inch le than the annual rainfall in Nahville How much le did Nahville get than Miami
Answers
Nashville gets 13.8 units of rainfall less than Miami.
We have to give that,
The annual rainfall in Albany is 0.33 inches less than the annual rainfall in Nashville.
Here, Miami's rainfall is 61.05 inches
Albany's rainfall is 46.92 inches.
Let the rainfall in Nashville be x units.
So, rainfall in Albany is,
x - 0.33
Now Albany gets 46.92 units of rainfall.
So, Nashville gets,
46.92 = x - 0.33
x = 46.92 + 0.33
x = 47.25 units
And Miami gets 61.05 units of rainfall.
So, Nashville gets,
61.05 - 47.25
= 13.8 units
Hence, Nashville gets 13.8 units of rainfall less than Miami.
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A company which uses the revaluation model for its PPE bought a building on 1 January 2014 for £50m. The building has an estimated useful life of 50 years and nil residual value. On 31 December 2018, the building was revalued at £40.5m and on 31 December 2020 it was revalued for a second time at £39m. The company uses the straight-line method of depreciation for all PPE items. There was no change to the remaining useful life after each revaluation. What is the net effect of both revaluations on the statement of comprehensive income?
Answers
Answer:
The net effect of both revaluations on the statement of comprehensive income is a net revaluation loss of £4.20m that will reduce the comprehensive income by the exact amount of £4.20m.
Step-by-step explanation:
This can be determined using the following 3 steps:
Step 1: Calculation of the effect of first revaluation: from 01 January 2014 to 31 December 2018
Building cost = £50
Number of useful life = 50
Revalued amount on 31 December 2018 = £40.5m
Annual depreciation expenses from 01 January 2014 to 31 December 2018 = Building cost / Number of useful life = £50m / 50 = £1m
Number of years from 01 January 2014 to 31 December 2018 = 5
Total depreciation expenses from 01 January 2014 to 31 December 2018 = Annual depreciation expenses from 01 January 2014 to 31 December 2018 * Number of years from 01 January 2014 to 31 December 2018 = £1m * 5 = £5m
Net book value on 31 December 2018 = Building cost - Total depreciation expenses from 01 January 2014 to 31 December 2018 = £50m - £5m = £45m
Revaluation loss from the first revaluation = Net book value on 31 December 2018 - Revalued amount on 31 December 2018 = £45m - £40.5m = £4.50m
Step 2: Calculation of the effect of second revaluation: from 01 January 2019 to 31 December 2020
Revalued amount on 31 December 2020 = £39m
Number of useful life remaining after 31 December 2018 = Number of useful life - Number of years from 01 January 2014 to 31 December 2018 = 50 - 5 = 45
Annual depreciation expenses from 01 January 2019 to 31 December 2020 = Revalued amount on 31 December 2018 / Number of useful life remaining after 31 December 2018 = £40.5m / 5 = £0.90
Number of years from 01 January 2019 to 31 December 2020 = 2
Total depreciation expenses from 01 January 2019 to 31 December 2020 = Annual depreciation expenses from 01 January 2019 to 31 December 2020 * Number of years from 01 January 2019 to 31 December 2020 = £0.90 * 2 = £1.80
Net book value on 31 December 2020 = Revalued amount on 31 December 2018 - Total depreciation expenses from 01 January 2019 to 31 December 2020 = £40.5m - £1.80 = £38.70m
Revaluation surplus from the second revaluation = Revalued amount on 31 December 2020 – Net book value on 31 December 2020 = £39m - £38.70 = £0.30m
Step 3: Calculation of the net effect of both revaluations on the statement of comprehensive income
Net revaluation loss = Revaluation loss from the first revaluation - Revaluation surplus from the second revaluation = £4.50m - £0.30m = £4.20m
Therefore, the net effect of both revaluations on the statement of comprehensive income is a net revaluation loss of £4.20m that will reduce the comprehensive income by the exact amount of £4.20m.
The net effect of the revaluations on December 31, 2018 and December 31, 2020 is that the comprehensive income will reduce by £11 million.
Data and Calculations:
Cost of PPE on January 1, 2014 = £50 million
December 31, 2018:
Revaluation amount = £40.5 million
Revaluation Loss = £9.5 million (£50 million - £40.5 million)
New book value = £40.5 million
December 31, 2020:
Revaluation amount = £39 million
Revaluation Loss = £1.5 million (£40.5 million - £39 million)
New book value = £39 million
Total Revaluation Loss = £11 million (£9.5 + £1.5 million)
Thus, the net effect of both revaluations on the company's statement of comprehensive income is reduction of £11 million.
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Julia correctly estimated the value of 183+ (76-15) +29 by rounding each number to the nearest ten. What was
Julia's estimation?
02
0 0 0 0
3
32
O 33
Answers
Julia's estimation for the expression 183 + (76 - 15) + 29, when Rounding each number to the nearest ten, is 270.
To determine Julia's estimation, we need to round each number to the nearest ten and perform the calculation.
Rounding each number to the nearest ten:
183 rounds to 180
76 rounds to 80
15 rounds to 20
29 rounds to 30
Now, let's perform the calculation using the rounded numbers:
183 + (76 - 15) + 29
= 180 + (80 - 20) + 30
= 180 + 60 + 30
= 240 + 30
= 270
Therefore, Julia's estimation for the expression 183 + (76 - 15) + 29, when rounding each number to the nearest ten, is 270.
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What is 1015
10
15
written in lowest terms?
ILL GIVE BRAINLIEST TO WHOEVER GETS IT RIGHT
Answers
Answer:
2/3
Step-by-step explanation:
....................
In the diagram below, each straight line of
three numbers has a total sum of 3552.
What number should replace the question
mark?
628
1745
342
?
Answers
The missing number in the diagram could be either 623 or 311, depending on the specific context or rules of the puzzle.
To find the missing number in the diagram, we can observe that each straight line of three numbers has a total sum of 3552. Let's analyze the given numbers:
Line 1: 628 + 1 + 7 = 636
Line 2: 8 + 1 + 4 = 13
Line 3: 5 + 3 + 4 = 12
Line 4: 2 + ? + ? = ?
To maintain the sum of 3552 for each line, we can subtract the sum of the known numbers from 3552 to find the missing values.
3552 - 636 = 2916
3552 - 13 = 3539
3552 - 12 = 3540
The difference between the known sums and the desired total sum is as follows:
2916 - 3539 = -623
3540 - 3539 = 1
Since the total sum for Line 4 must be 3552, we can deduce that the two missing numbers must add up to 623. Given that the numbers in the diagram are integers, the possible combination of two numbers is 623 and 0, or 311 and 312.
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