The 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 as calculated from the given data is 5.20 and 7.60.
The confidence interval for the difference of the population mean is calculated as,
CI = ( x1 - x2 ) +- z x √SD1²/n1 + SD2²/n2
= ( 82.9 - 76.5) +- 1.96 x √7.97²/293+ 6.66²/n2.82
=6.4 ± 1.199
=(v5.201 , 7.599)
therefore , approximately 5.20 , 7.60 .
Therefore , the confidence interval between them is found to be as , ( 5.20 , 7.60 ) answer.
The confidence interval is a calculation based on the statistics of the observed data that estimates the amount of uncertainty associated with a sample.
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In how many ways can Harold, Steve, John, Roslyn, Marian and Connie line up so that no two of Harold, Steve and John are next to each other ?
There are four general arrangents of boy/girl to consider:
BGBGBG, GBGBGB, BGGBGB, and BGBGGB.
For any one of these four basic arrangements, the boys can be
rearranged (permuted) among themselves in 3 × 2 × 1 = 6 different
ways. Similarly, the three girls can be rearranged among
themselves in 6 ways. Since the boys and girls can be rearranged
independently, the number of ways to create any one of the four
basic arrangements is 6 × 6 = 36.
So the total number of ways that 3 boys and 3 girls can line up so
that no two of the three boys are next to each other is
4 × 36 = 144 .
The total number of ways that 3 boys and 3 girls can line up so that no two of the three boys are next to each other is found to be as 144 .
It is given that there are four general arrangements of boys and girls,
Here, the boys can be arranged or rearranged (permuted) among themselves in a total of , 3 × 2 × 1 = 6 different ways.
Similarly, the three girls can be rearranged among
themselves in 6 ways.
We are given that both the groups can arrange themselves independently .
Therefore, the number of ways to create any one of the four basic arrangements is 6 × 6 = 36.
Therefore, the number of ways to arrange them is ,
4 × 36 = 144 .
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Multiply.
Your answer should be a monomial in standard form.
{(4z^3)(-3z^3)}=(4z
3
)(−3z
3
)
The required simplified expression as a monomial is given as -12[z⁶].
What is a polynomial function?A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.
here,
Given an expression, the outcome of the multiplicative depression will be an expression of a monomial.
= [4z³][-3z³]
= 4 × 3 [-z ³⁺³]
= -12[z⁶]
Thus, the required simplified expression as a monomial is given as -12[z⁶].
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I don't know HOW TO DO THIS
Answer:
sorry, I forget how to do the other ones and I'm just as confused but for 4. AD is 20 and 5. GJ is 17
Step-by-step explanation:
4. side AD is equal to side CD so therefore its 20.
5. side are equal again so make
4x+5 = 2x+11
-5 -5
4x = 2x+6
-2x -2x
2x = 6
/3 /3
x = 3
2(3)+11
6+11
17
(b) Felipe is deciding how many people to take to the movies. The table below
shows the cost for different sized groups of people.
Check
Number in group
Cost (in dollars)
2
10
3 9
15 45
The cost for each person is not always the same.
OThe cost for each person appears to be the same.
Predicted number in group for a cost of $50:
Answer:
Step-by-step explanation:
from the form we know, 10/2=15/3=45/9=5.so we need select the second choice, the number of group 50 dollar is 50/5=10
the anwser is second choice, fill 10 in blank.
if u like this, pls 5 stars. tku!
Simplify as far as possible. 2 √ 3 + 2 √ 27
The required simplified solution of the given expression is 8√3.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
= 2 √ 3 + 2 √ 27
Since √27 = 3√3
= 2√3 + 2× 3√3
= √3 [2 + 6]
= √3[8]
= 8√3
Thus, the required simplified solution of the given expression is 8√3.
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Phyllis invested $10,500, a portion earning a simple interest rate of
3 1/2% per year and the rest earning a rate of 3% per year. After one year the total interest earned on these investments was $352. 50. How much money did she invest at each rate?
Please answer ASAP
The money invested by Phyllis with simple interest rate 3 1/2% and 3% per year is given by $7500 , and $3,000 respectively.
As given in the question,
Total amount with Phyllis is equal to $10,500
Let 'x' be the portion of Phyllis earning invested with 3 1/2% per year simple interest rate
Then $( 10,500 - x ) invested by Phyllis with simple interest rate 3% per year
Total interest earned by the investment = $352.50
0.035x + 0.03( 10,500 - x ) = $352.50
⇒0.035x + 315 - 0.03x = 352.50
⇒0.005x = 352.50 - 315
⇒0.005x = 37.5
⇒x = $7500
and $( 10,500 - x ) = $( 10,500 - 7500 )
= $ 3,000
Therefore, the amount of invested with simple interest rate 3 1/2% per year and 3% is equal to $7500 and $3,000 respectively.
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Zendaya has $540 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $269.88.
She buys 4 bicycle reflectors for $10.57 each and a pair of bike gloves for $17.76.
She plans to spend some or all of the money she has left to buy new biking outfits for $65.65 each.
Write and solve an inequality which can be used to determine
x
x, the number of outfits Zendaya can purchase while staying within her budget.
Plsss help!!
Answer:
269.88 +4(10.57) +17.76 +65.65x ≤ 540x ≤ 3.2; 3 outfits or lessStep-by-step explanation:
After spending $269.88, 4 times $10.57, and $17.76 of her $540 budget, you want to know how many (x) outfits Zendaya can buy at $65.65 each.
InequalityThe total of Zendaya's spending must be no more than her budget amount:
269.88 +4(10.57) +17.76 +65.65x ≤ 540
SolutionSimplifying the inequality gives ...
329.92 +65.65x ≤ 540
65.65x ≤ 210.08 . . . . . . . . . . subtract 329.92
x ≤ 3.2 . . . . . . . . . . . . . divide by 65.65
Zendaya can purchase up to 3 outfits while staying within her budget.
y2−10y+24+6x−9x2
[tex]factorization[/tex]
Answer:
y(2-10)2(12+3x)...
Step-by-step explanation:
first make groups of the numbers
y2 with 10 y they both have y in common
so you can write it as y(2-10)
after 24 with 6x they both have 2in common (2×12=24)
so you can write it as 2(12+3x)
and you can do the rest with the same technique
The times taken by 25 people to complete a puzzle are shown. Draw a frequency polygon for data.
To create a frequency polygon calculate the midpoint, locate the midpoints and connect them with lines.
What is a frequency polygon?A frequency polygon is a form of graph that shows how frequently a particular variable—in this case, the amount of time it takes for people to finish a puzzle—occurs.
So, we must determine the midpoint or average of the range for each category.
0 < t < 10 = 5
10 < t < 20 = 15
20 < t < 30 = 25
30 < t < 40 = 35
2. Add a point where the data of the axis Y and X form an intersection.
3. Connect the points.
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Nicole randomly selects a red card from a standard deck of cards. What outcome is the complement of drawing a red card?
Selecting an ace
Selecting a heart
Selecting a face card
Selecting a black card
The complement of the event: "drawing a red card" is the last option:
"Selecting a black card"
What outcome is the complement of drawing a red card?The complement of an event is the set of all the outcomes such that the original event is false.
For example, the complement of drawing a red card, would be "not drawing a red card"
We know that there are two types of coloes, black and red.
Then "drawing a black card" is equivalent to "not drawing a red card"
Thus, the complement is the last option:
"Selecting a black card"
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A store that specializes in shipping packages reports that the distribution of packages shipped during the winter holidays is normally distributed with a mean of 4. 5 pounds with a standard deviation of 1. 8 pounds
What is the probability that two randomly selected packages are both more than 4. 5 pounds? (assume the packages are independent of each other)
a. ) 0. 5
b. ) 1
c. ) 0
d. ) 0. 25
The correct option is option (d).
To solve this problem, we need to find the probability that two randomly selected packages are both more than 4.5 pounds. Since the distribution is normal, we can use the standard normal distribution table to find the probability.
The first step is to standardize the weight of the packages by subtracting the mean from the weight and dividing it by the standard deviation. The weight of 4.5 pounds is the mean, so the standardized weight is (4.5 - 4.5) / 1.8 = 0.
The probability that a package weighs more than 4.5 pounds is the same as the probability that a standardized package weighs more than 0. This probability is equal to 1 - P(Z < 0) , where Z is the standardized weight.
Using a standard normal distribution table, we find that P(Z < 0) = 0.5. Therefore, the probability that a package weighs more than 4.5 pounds is 1 - 0.5 = 0.5.
Since the two packages are independent, we can find the probability that both packages are more than 4.5 pounds by multiplying the probability of one package being more than 4.5 pounds by itself. So, the probability that two randomly selected packages are both more than 4.5 pounds is 0.5 * 0.5 = 0.25.
In conclusion, the probability that two randomly selected packages are both more than 4.5 pounds is 0.25
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How many variable terms are in the expression 3x3y 5x2 Y 9?
The variable terms in the expression 3[tex]x^{3}[/tex]y + 5[tex]x^{2}[/tex] + y + 9 are [tex]x^{3}[/tex]y, [tex]x^{2}[/tex], and y.
The expression provided is
3[tex]x^{3}[/tex]y + 5[tex]x^{2}[/tex] + y + 9
In the expression, each variable is represented by a letter.
Let's look at the variables for each term.
The variable in the first term, 3[tex]x^{3}[/tex]y, is [tex]x^{3}[/tex]y.
The variable in the second term, 5[tex]x^{2}[/tex] , is [tex]x^{2}[/tex] .
Y is the variable in the third term.
There is no variable in term 9's final equation.
The variables in the expression are [tex]x^{3}[/tex]y, [tex]x^{2}[/tex] , and y.
As a result, the variables [tex]x^{3}[/tex] and y are the variable terms.
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The sum of the measures of the interior angles of a convex polygon is 1260°. Classify the polygon by the number of
sides.
O Heptagon
O Octagon
ONonagon
O Decagon
The polygon presented will have nine sides. This suggests that a nonagon is the necessary polygon.
How can you determine a polygon's entire angle?Divide the number of triangles in the polygon by 180° to determine the sum of its inner angles. Where is the number of sides, the formula for computing the sum of internal angles is (n 2) 180. In a regular polygon, all internal angles are equal.
What is the formula for polygons?The following are crucial polygon formulas: A polygon with "n" sides has a total interior angle sum of 180 degrees (n-2) A "n-sided" polygon has [n(n-3)]/2 diagonals. A regular n-sided polygon's internal angles are measured as [(n-2)180°]/n.
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7. Communicate and justify Janice is dividing
1.926. Why does she exchange the
place-value blocks shown for 18 tenths and
12 hundredths?
The answers to these partial divisions add up to 30 + 2 = 32, or 192/6. We can calculate the solution by dividing 32 by 100, or 0.32, to get 1.92/6.
What do we mean by an exchange?The formula for computing 1.92 divided by 6 is 1.92 multiplied by 100, divided by 100, and then multiplied by 1.92. There are 18 tenths and 12 ones in 1.92*100 = 192, which is the result. Due to the fact that both 18 and 12 are multiples of 6, this representation is practical.
Then, we can divide 18 tenths by six to get three tenths (30), and we can divide 12 ones by six to get two ones (2). 30 + 2 = 32, or 192/6, is the result of adding the answers to these partial divisions. To get 1.92/6, divide 32 by 100, which is 0.32, and that gives us the answer.
The complete question is:
Janice is dividing 1.92 divided by 6. Why does she exchange the place value blocks shown for 18 tenths and 12 ones ?
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The answers to these partial divisions add up to 30 + 2 = 32, or 192/6. We can calculate the solution by dividing 32 by 100, or 0.32, to get 1.92/6.
What do we mean by an exchange?The formula for computing 1.92 divided by 6 is 1.92 multiplied by 100, divided by 100, and then multiplied by 1.92. There are 18 tenths and 12 ones in 1.92*100 = 192, which is the result. Due to the fact that both 18 and 12 are multiples of 6, this representation is practical.
Then, we can divide 18 tenths by six to get three tenths (30), and we can divide 12 ones by six to get two ones (2). 30 + 2 = 32, or 192/6, is the result of adding the answers to these partial divisions. To get 1.92/6, divide 32 by 100, which is 0.32, and that gives us the answer.
The complete question is:
Janice is dividing 1.92 divided by 6. Why does she exchange the place value blocks shown for 18 tenths and 12 ones ?
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What is associative property example?
The example of an associative property is a+(b+c) = (a+b) + c for additional operation and a × (b × c) = (a × b) × c for the multiplication operation. The associative property is used to solve an equation or expression of real numbers.
What are the properties of real numbers?
In the number system, real numbers are only the fusion of rational and irrational numbers. These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.
The four primary characteristics of real numbers are as follows:
Commutative property
Associative property
Distributive property
Identity property.
Associative property: The associative property is applicable on two arithmetic operations. They are multiplication and addition.
For multiplication operations: a × (b × c) = (a × b) × c
For additional operation: a+(b+c) = (a+b) +
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Estimate how many times larger 1.9 • 10^-8 is than 4.2 • 10^-13
Answer:
Step-by-step explanation:
a.[tex]1.9[/tex]·[tex]10^{-8}[/tex]=190000·[tex]10^{-13}[/tex]
b.so 190000÷4.2=4523
c.finally, about 4523 times
4. Automotive Trades At the beginning of the day on Monday, the parts
department has on hand 520 spark plugs. Mechanics in the service depart-
ment estimate they will need about 48 plugs per day. A new shipment of
300 will arrive on Thursday. Write out a mathematical statement that gives
the number of spark plugs on hand at the end of the day on Friday. Calcu-
late this total.
StS estimate
Therefore , the solution of the given problem of equation comes out to be 580 spark plugs will be left.
Describe the equation.Using the equals symbol (=), a mathematical equation appears to be a formula that connects two statements and denotes equality. A scientific assertion that supports the equality of two mathematical abstraction is known as an equation in algebra. For instance, the equal sign is present between the variables ptdc + 6 and 12 in the output obd + 6 = 12. The link between the syllable on either side of either a letter is described by a mathematical formula. In many cases, the logo and the say — are identical.
Here,
Given: A new supply of 300 spark plugs will come on Thursday,
and 520 spark plugs require 48 plugs per day.
To determine an equation to determine however many plugs will just be left at the end of Friday:
So,
where n is the no of days
=> 520 - 48*n + 300
=> 520 - 48*5 + 300
=> 520 - 240 + 300
=> 520 + 60
=> 580
Therefore , the solution of the given problem of equation comes out to be 580 spark plugs will be left.
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DEFG is a square with vertices at D(1, 1), E(1,6), F(6, 6), and G(6, 1). DEFG is reflected in the line x = 1. Find the coordinates of
D',E,F, and G'.
By considering the reflection, the coordinates of the reflected square D'E'F'G' are:
D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)
What is square?A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a type of rectangle, but with all sides equal. The opposite sides of a square are parallel and of equal length. A square can be defined by its side length or by the coordinates of its vertices.
What is reflection?Reflection is a type of transformation in geometry in which a shape is flipped over a given line, called the line of reflection. The image that is created is a mirror image of the original shape. The line of reflection can be a horizontal line, a vertical line, or any line that is not parallel to the axes. Reflecting a shape over a line involves taking the coordinates of each point of the shape and applying a specific rule (such as multiplying or adding a constant) to the x or y coordinate, depending on the line of reflection. This rule is often simple and easy to apply, such as reflecting over x = 1. The reflected shape will be in the same plane as the original shape but with a different orientation or position.
When a square is reflected in the line x=1, each of the points on the square will have their x-coordinate replaced by 1 subtracted from their original x-coordinate.
The coordinates of the reflected square D'E'F'G' can be found by applying this rule to the original coordinates of square DEFG:
D(1,1) => D'(1-1,1) => D'(0,1)
E(1,6) => E'(1-1,6) => E'(0,6)
F(6,6) => F'(6-1,6) => F'(5,6)
G(6,1) => G'(6-1,1) => G'(5,1)
So the coordinates of the reflected square D'E'F'G' are:
D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)
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A corporation earned a profit of $2.5 x 104 for 1 x 10³ days in a row. What was the corporation's total profi
during this time period?
Total profit earned = 25000000 dollars
What is profit?Profit is a financial achievement which is the difference between the amount of money or resources people earned and the amount is spent in various purpose. In case of a business organization, the difference between production and cost is termed as profit. Let, someone invested money for operating business, he needs to spend money for workers, for the welfare of business and after all these he has amount that comes from business that is called profit.
What is the total profit during this time period?Given, profit earned = $ 2.5 × 10⁴ in the 1×10³ days in a row
total profit earned during this time = $(2.5 × 10⁴ × 10³)
$2.5 × 10⁷
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I have 2 bags of onion bhajis, one of which holds 42 bhajis. I empty them
onto a plate, making 50 bhajis. How many bhajis were in the second bag?
There were 8 bhajis in the second bag if he have 2 bags of onion bhajis, one of which holds 42 bhajis.
What is an equation ?
In mathematics, an equation is a statement that asserts the equality of two expressions, typically containing one or more variables. Equations are often written in the form of "expression = expression" or "expression - expression = 0"
Let's call the number of bhajis in the second bag "x".
We know that he total number of bhajis after emptying both bags onto the plate is 50.
So we can write an equation:
42 + x = 50
To solve for x, we can subtract 42 from both sides:
x = 50 - 42
x = 8
Therefore, there were 8 bhajis in the second bag.
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By choosing an appropriate line, use the
diagram to estimate the solutions to these
simultaneous equations:
2
y = -x +1.5
y = 1.5x2.5
So on solving the provided question, here we can say that by is a simultaneous equations the value of x = - 3/5 and y = 9/10
What is the simultaneous equation formula?Multiple algebraic equations that have the same unknowna as the give in the variables and the same answer are referred to as simultaneous equations. This suggests that there is a single solution to the simultaneous equations. Examples of simultaneous equations include: 2x - 4y = 4, 5x + 8y = 3, and others. This implies that the simultaneous equations have a single solution. The simultaneous equations 2x - 4y = 4, 5x + 8y = 3, and others are examples.
y = -x + 1.5
y = 1.5x + 2.5
x = -3/5
y = 9/10
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What is the importance of constructing a probability distribution for a random variable in interpreting data?
A probability distribution model is a guide you use to fit a random variable in order to generalize its behavior.
A probability distribution is a list of all of the possible outcomes of a random variable, along with its corresponding probability values.
A probability distribution links each outcome of a random variable or process with its probability of occurrence.
A probability distribution model is a guide you use to fit a random variable in order to generalize its behavior.
These models have a mathematical background, and can be very picky. For them to work properly, the random variable you are trying to fit in must meet different assumptions so that the outcomes of the model have the correct probabilities, and also so that you can test and validate the model against real data from the random variable.
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What is the value of the expression below if
x = -5, h = -5, and y = -3.
3-h(x+4)-2y
Answer:
4
Step-by-step explanation:
3 - h(x + 4) -2y Substitute in what was given.
3 -(-5)(-5+4)-2(-3)
3 + 5(-1) + 6
3-5+6
-2+6
4
Answer:
3-(-5)(-5+4)-2(-3)
3+5(-1)+6
3-5+6
-2+6
4
Each of Frank's notebooks is 2/5 inches wide. If he has 10 inches of space remaining on his bookshelf, how many notebooks will fit
We can fit 25 notebooks on the space.
Now, According to the question:
The width of the notebook is 2/5
The length of the space is 10 inches.
To find the number of the notebooks can put there divide 30 by 2/3
Number of the books : [tex]\frac{10}{\frac{2}{5} }[/tex] = 10 × [tex]\frac{5}{2}[/tex]
=> 50/2 = 25
The number of the notebook is 25
We can fit 25 notebooks on the space.
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Tara placed the numbers -2 1/6, 3/11 and 2 2/9 on the number line below. Which letters
represent the correct location for each number?
-2 1/6 is A, 3/11 is C, and 2 2/9 is E
or
-2 1/6 is A, 3/11 is D, and 2 2/9 is E
or
-2 1/6 is A, 3/11 is D, and 2 2/9 is F
or
-2 1/6 is B, 3/11 is D, and 2 2/9 is F
Answer:
sorry beacuse I don't know anything
help help help help help
please answer all 3 questions thank you~!!!!
Answer:
X of M is 6, Y of M is 4, Pair is (6,4)
Step-by-step explanation:
M = 6
M = 4
M (6,4)
Triangle STU is a right triangle.
Write an equation that relates the lengths of sides s, t, and u? (5 points)
HELP!!!
Marta bakes 3 types of cake: chocolate, fruit, and sponge. The recipe for each cake includes flour and sugar and she uses 3.3kg of flour and 3.1kg of sugar in total.
Each chocolate cake uses 225 g of flour and 300g of sugar
Each fruit cake uses 320g of flour and 250g of sugar
Each sponge cake uses 400 g of flour and 325g of sugar
Marta sells chocolate cakes for $12, fruit cakes for $10, and sponge cakes for $8 and makes a total of $114
How many of each cake does she make?
(Answer in the back of the book: 4 chocolate, 5 fruit, 2 sponge cakes)
The three equations for this problem are:
The total amount of flour used: 3.3kg = (225g/cake) * (number of chocolate cakes) + (320g/cake) * (number of fruit cakes) + (400g/cake) * (number of sponge cakes)The total amount of sugar used: 3.1kg = (300g/cake) * (number of chocolate cakes) + (250g/cake) * (number of fruit cakes) + (325g/cake) * (number of sponge cakes)The total revenue from sales: $114 = ($12/cake) * (number of chocolate cakes) + ($10/cake) * (number of fruit cakes) + ($8/cake) * (number of sponge cakes)Let's call the number of chocolate cakes x, the number of fruit cakes y, and the number of sponge cakes z
so the
first equation can be written as 3.31000 = (225x) + (320y) + (400z)second 3.11000 = (300x) + (250y) + (325z)and third one 114 = (12x) + (10y) + (8*z)let's use the third equation to get the value of x,y and z:
x = (114 - 10y - 8z) / 12y = (114 - 12x - 8z) / 10z = (114 - 12x - 10y) / 8If you get the values and substitute, then the answer would be:
4 chocolate cakes, 5 fruit cakes, 2 sponge cakes
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i need the correct answer only 2 try’s and due in 15 min
The sample space between A to C is A,B,C
What is the probability?The likelihood that a sample point will occur is quantified by its probability.
The likelihood of a sample point
According to tradition, statisticians have adopted the following guidelines.
Any sample point's probability can be between 0 and 1.
The probability of every sample point in a sample space added together is 1.
Let's say we run a straightforward statistical experiment. One coin is flipped. Heads or tails are the possible results of the coin flip. These results taken as a whole serve as our experiment's sample space. Each result stands in for a single sample point in the sample space. What is each sample point's probability?
Solution: the total of all sample points' probability
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