Using a left-hand approximation means that we will use the left endpoint of each interval to approximate the area under the curve.
a) Using 4 boxes:
The interval from 0 to 2 can be divided into 4 equal parts, so each part has a length of 0.5.
The height of each box will be the value of y at the left endpoint of each interval.
The area of each box can be calculated as follows:
For the first box, the left endpoint is (0, 1) and the height is 2(0) + 1 = 1. The area is 0.5 * 1 = 0.5.
For the second box, the left endpoint is (0.5, 2) and the height is 2(0.5) + 1 = 2.5. The area is 0.5 * 2.5 = 1.25.
For the third box, the left endpoint is (1, 3) and the height is 2(1) + 1 = 3. The area is 0.5 * 3 = 1.5.
For the fourth box, the left endpoint is (1.5, 4) and the height is 2(1.5) + 1 = 4.5. The area is 0.5 * 4.5 = 2.25.
The total area is the sum of the areas of all the boxes, so the total area is 0.5 + 1.25 + 1.5 + 2.25 = 5.
b) Using 8 boxes:
The interval from 0 to 2 can be divided into 8 equal parts, so each part has a length of 0.25.
The height of each box will be the value of y at the left endpoint of each interval.
The area of each box can be calculated as follows:
For the first box, the left endpoint is (0, 1) and the height is 2(0) + 1 = 1. The area is 0.25 * 1 = 0.25.
For the second box, the left endpoint is (0.25, 2.5) and the height is 2(0.25) + 1 = 2.5. The area is 0.25 * 2.5 = 0.625.
For the third box, the left endpoint is (0.5, 3) and the height is 2(0.5) + 1 = 3. The area is 0.25 * 3 = 0.75.
And so on, for all 8 boxes.
The total area is the sum of the areas of all the boxes, so the total area is 0.25 + 0.625 + 0.75 + ... + 3.375 = 5.125.
So, the area between the x-axis and the curve y = 2x + 1 on the interval (0, 2) can be approximated as 5 or 5.125 depending on the number of boxes used.
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The length of a rectangle is 11 ft more than double the width, and the area of the rectangle is 63 ft^2. Find the dimensions of the rectangle.
The dimensions of the rectangle are width = 3.5 feet and length = 18 feet.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Area of the rectangle is 63 ft².
The length of a rectangle is 11 ft more than double the width.
let the width be x.
So, the length is 2x + 11.
So, Area of rectangle = 63 ft².
l x w = 63
(2x+ 11) x = 63
2x² + 11x = 63
2x² + 11x - 63 =0
On solving the above Quadratic equation we get
x = 7/2 and -9.
So, the width is 3.5 feet and length = 2(3.5) +11 = 18 feet
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Expand the expression 8(x-4)
Which of the following is true?
Group of answer choices
three and three ninths plus seven and six elevenths equals ten and eighty seven ninety ninths
two and three eighths plus six and four fifths equals eight and twelve fourtieths
three and three sevenths plus four and two thirds equals seven and two twenty ones
four and five sixths plus five sevenths equals nine and ten thirteenths
Answer:
three and three ninths plus seven and six-elevenths equals ten and eighty-seven ninety ninths
Step-by-step explanation:
Pls mark me brainliest
(Three-Column Tables MC)
A three-column table is given
Part A C D
Part 14 28 63
Whole 20 40 B
What is the value of B in the table?
A:60
B:75
C:80
D:90
The value of B on the table is given as follows:
D. 90.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
From the table, the constant is obtained as follows:
k = 20/14 = 40/28 = 10/7.
Hence the relationship is given as follows:
y = 10x/7.
The value of B is the value of y when x = 63, hence:
y = 10 x 63/7
y = 10 x 9
y = 90.
Meaning that the correct option is given by option D.
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The testing times for a group of college students were normally distributed with a mean of 32 minutes and a standard deviation of 2.1 minutes.
The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation.
Fill in the indicated boxes.
Used the Empirical Rule to complete the following statements:
68% of testing times were between
minutes and
minutes.
95% of testing times were between
minutes and
minutes.
99.7% of testing times were between
minutes and
minutes.
50% of testing times were below
minutes.
The complete statements are:
68% of the data between 34 and 42 minutes.95% of the data between 30 and 46 minutes.99.7% of the data between 26 and 50 minutes.50% of the data between 38 minutes.What is Standard Deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
Mean= 32 minutes
Standard deviation = 2.1 minutes
So, [tex]\mu[/tex]- 3[tex]\sigma[/tex] = 38 - 3x 4= 26
[tex]\mu[/tex]- 2[tex]\sigma[/tex] = 38 - 2x 4 = 30
[tex]\mu[/tex]- [tex]\sigma[/tex] = 38 -4 =34
[tex]\mu[/tex]=38
[tex]\mu[/tex]+ [tex]\sigma[/tex] = 38+ 4= 42
[tex]\mu[/tex]+ 2[tex]\sigma[/tex]= 46
[tex]\mu[/tex]+ 3[tex]\sigma[/tex]=50
Thus, 68% of the data between 34 and 42 minutes.
95% of the data between 30 and 46 minutes.
99.7% of the data between 26 and 50 minutes.
50% of the data between 38 minutes.
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EASY POINTS!
Let's say you are ordering books online and the online store is having a 12% off sale. If the subtotal of the books, before the discount, is $25, what is the total cost of the books if there is also a state sales tax of 7.5%?
$23.65
$23.13
$26.13
$22.00
Answer:
$23.13
Step-by-step explanation:
The subtotal of the books before the discount is $25. To calculate the value, you multiply $25 by 12% (0.12), which equals $3. So the total cost of the books after the discount is $25 - $3 = $22.
Next, to calculate the cost of the books, including the state sales tax, you would multiply $22 by 7.5% (0.075), which equals $1.65.
Therefore, the total cost of the books, including the state sales tax is $22 + $1.65 = $23.65
Which of the following variables are categorical and which are numerical? If the variable is numerical, then specify whether the variable is discrete or continuous. a. Colors of cars in a mall parking lot. - Categorical - Numerical; discrete - Numerical; continuous b. Time it takes each student to complete a final exam.
- Categorical - Numerical; discrete - Numerical, continuous c. The number of patrons who frequent a restaurant. - Categorical - Numerical; discrete - Numerical continuous
The Variable "Colors of cars in a mall parking lot" is (a) categorical variable and not a numerical variable.
A Categorical Variable is defined as a type of variable which takes on one of a limited, and usually fixed, number of possible values.
In this case, the possible values are different colors of cars such as red, blue, green, etc. Categorical variables are also known as nominal variables because they do not have an inherent order or mathematical meaning.
a Categorical variables are different from Numerical Variables, which are variables that have a numerical value that can be used to perform mathematical operations.
The given question is incomplete , the complete question is
Which variables is categorical and which are numerical ? If the variable is numerical, then specify whether the variable is discrete or continuous.
Colors of cars in a mall parking lot. -
(a) Categorical
(b) Numerical - Continuous
(b) Numerical - Discrete
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the length of a rectangle is 4 times the width. if the area of the rectangle is 324 square feet, the dimensions of the rectangle are ?
If the area of the rectangle is 324 square feet, the dimensions of the rectangle are length 9 feet and width 36 feet.
A rectangle with an area of 324 square feet and a length that is 4 times the width can be described by the equation W * 4W = 324. This equation can be expanded to 4W^2 = 324.
To find the width of the rectangle, we can take the square root of both sides of this equation, which gives W^2 = 81. Taking the square root of 81 gives W = 9 feet, which is the width of the rectangle.
Since the length of the rectangle is 4 times the width, the length of the rectangle is 4 * 9 = 36 feet. So the dimensions of the rectangle are 9 feet by 36 feet.
This means that if you draw a rectangle with a width of 9 feet and a length of 36 feet, the area of this rectangle would be 324 square feet.
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7,11,2,18,-7
What's the next number in this sequence and how did you arrive at that number
The last term of the missing pattern is 57.
What is Sequence?A sequence is a list of items where repetitions are allowed and hierarchy is crucial. The same as a set, it has members. The number of items determines how long the sequence is.
Given:
Sequence: 7,11,2,18,-7
As, the difference between the first two-term is 4,
while in the next two-term is 16(4²),
So, in the next two-term the difference will be equal to 64(4³).
Then, the last term is
x- (-7)= 64
x+ 7= 64
x= 57
Hence, the last term is 54.
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What are the numbers?
10 and 35 are the numbers that divides 78 with remainder 8.
What is Division?A division is a process of splitting a specific amount into equal parts.
Dividend is the number that is to be divided by the divisor.
Divisor is the number by which the dividend is to be divided is called the divisor.
Quotient is the resultant of the division is called the quotient.
Remainder is the number that is left after division is called the remainder
78/10
70/10+8
and 78/35 which gives 70/35+8
Hence, 10 and 35 are the numbers that divides 78 with remainder 8.
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please help me with this problem i’ll give you brainlist!!
Any line can be graphed using two points. By entering two x x values into the equation, you can determine the associated y y values.
What is the information graph can provide?Graphs offer a visual means of presenting complex data and demonstrating the link between various variables or data sets. Using graphs is a great approach to show patterns and connections in the data.
Because they are brief and to the point, they let readers visually analyze any data and serve as a quick review of the information given.
An informative text's graph consistently follows the information given within the text's purview. There is no emphasis on external texts or, say, exploration in these. This is also unhelpful.
y-3=2(x+1)
Solution to Equation ( - 1 , ? )
x = - 1
y = ?
Substitute x = - 1 in the equation
y - 3 = 2( -1 + 1)
=> y - 3 = 2(0)
=> y - 3 = 0
=> y = 3
Solution to Equation ( - 1 , 3 )
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if you only purchased 2 pairs of shoes at best shoes instead of the 4 described in problem 20, how much would you have paid, based on the average price
If he purchased only 2 pair of shoes, the amount he has to pay based on average price would be $34.62.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
The total bill for four pairs of shoes came to $69.24
Number of pairs of shoes = 2
We need to find the average price for each pair of shoes .
69.24=2x
x=34.62
Hence, the average price is $34.62.
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garnet has a container with 3 1/2 cups of flour of flour in it. She can make one dozen muffins with 2 1/2 cups of flour. How many dozens of muffins can garnet make with the flour she has?
The dozens of muffins that garnet can make with the flour she has is;
1²/₅
How to solve Fraction Word Problems?Let us begin by saying that one dozen is 12 and not a bakers dozen (13).
Thus, our solution will be arrived as by first seeing how many times 2¹/₂ can go into 3¹/₂ by dividing the two.
Let us first convert the mixed fractions to improper fractions to get;
2¹/₂ = 5/2
3¹/₂ = 7/2
Thus, the final step is;
7/2 ÷ 5/2
= 7/5
= 1²/₅
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A cell phone company estimates that a cell phone loses about 15% of its value each year after it is purchased. The function f(x)=900(0.85)^x represents the estimated value (in dollars) of a cell phone 5 years after its purchase. What is the domain and range?? PLEASE HURRY THIS IS DUE IN AN HOUR
The domain of the function f(x) = 900(0.85)^x is the set of real numbers, since the value of x (the number of years after purchase) can be any real number.
The range of the function is non-negative real numbers and less than 900, since the value of the function (the estimated value of the cell phone in dollars) will always be non-negative and less than the original price of 900 dollars, since it is losing value every year.
Step-by-step explanation:
In City A, 35% of all residence have at least 3 people living in the residence and in City B, 40%
of all residence have at least 3 people living in the residence. A residence will be selected from
each city. What is the probability that both residences have at least 3 people living in the
residence?
O 0.86
0.14
O 0.75
OL
2
(
(
The probability that both residences have at least 3 people living in
residence is 0,75. Answer: C
The probability that a residence selected from City A has at least 3 people living in it is 35%, and the probability that a residence selected from City B has at least 3 people living in it is 40%. To find the probability that both events occur (i.e., that both residences have at least 3 people living in them), you would multiply the individual probabilities:
0.35 * 0.40 = 0.75.
Answer: C
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Find the slope of the line described in the table.
m = 1/2
m = − 1/2
m = 2
m = - 2
The slope of the line described in the table is m=-1/2
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The points from the table are (-4, 3) and (-2, 2)
slope=2-3/-2+4
=-1/2
Hence, the slope of the line described in the table is m=-1/2
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How many letters do you need to name a point? a. One b. Two c. Three d. Four
The correct option is option(a) as only one letter is required to name a point.
What is a point?
A point in traditional Euclidean geometry is a simple concept that represents an exact place in space and has no length, breadth, or thickness. A point in modern mathematics is more broadly referred to as a component of a set known as a space. A point is an area that is depicted by a dot. A point just has a position; it lacks any dimensions such as length, width, shape, or size.
Usually, a geometrical figure is named by assigning one letter to each vertex of the figure.
So for a rectangle, it is 4 letters.
Hexagon is named using 6 letters since it has 6 vertices.
For a point, as mentioned there are no dimensions. It is just a dot.
Therefore a point is named using only one letter.
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 12 people took the trip. She was able to purchase coach tickets for $340 and first class tickets for $1220. She used her total budget for airfare for the trip, which was $8480. How many first class tickets did she buy? How many coach tickets did she buy?
She bought 7 first class tickets and 5 coach tickets. The solution has been obtained by using the linear equation.
What is a linear equation?
It is a linear equation that has the highest degree of one. This demonstrates that there aren't any variables in linear equations with exponents higher than one. A straight line is produced on the graph by such an equation.
Let the number of first class tickets be 'x' and coach tickets be 'y'.
We are given that total of 12 people took the trip.
So,
x + y = 12 ....(1)
Also, we are given that she was able to purchase coach tickets for $340 and first class tickets for $1220 and the total fare came out to be $8480.
So,
340x + 1220y = 8480 ....(2)
From (1), we get
x = 12-y
Substituting this in (2), we get
⇒340(12-y) + 1220y = 8480
⇒4080 - 340y + 1220y = 8480
⇒4080 + 880y = 8480
⇒880y = 4400
⇒y = 5
Therefore, x = 12-5 = 7
Hence, she bought 7 first class tickets and 5 coach tickets.
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How do i Simplify to a single power of 4
Drag each interval to a box to show if the function shown is increasing, decreasing, or neither over that interval.
I NEED HELP ASAP
Each interval that represents the behavior of the function are shown below:
0 < x < 4: increasing.
4 < x < 6: decreasing.
6 < x < 8: increasing.
8 < x < 10: decreasing.
10 < x < 14: neither increasing or decreasing.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
First, we need to know when the function is increasing, and when is decreasing.
It is because greater x-values correspond to higher y-values that a function increases. On the other side, a function decrements when lower y-values are associated with greater x-values. The function will move in the graph in an upward direction when it is rising and in a downward direction when it is decreasing.
So, according to the given graph, we see that between 0 and 4 is increasing, the higher x-values are, higher y-values are. Between 4 and 6 is decreasing, is downwards. Between 6 and 8 is increasing. Between 8 and 10 is decreasing. In finally, between 10 and 14 is neither decreasing or increasing, it remains horizontal.
All these interpretations we can expressed using math language, specifically inequalities:
0 < x < 4: increasing.
4 < x < 6: decreasing.
6 < x < 8: increasing.
8 < x < 10: decreasing.
10 < x < 14: neither increasing or decreasing.
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Complete question:
1/15 results in a repeating decimal.
Answer:
below
Step-by-step explanation:
1/15 = 1 divided by 15 = .06 (underlined part repeats)
Given the following functions:
f(x) = 2x+6
Find (h-f)(x).
○ 4x² - 3x + 7
O 4x² 2x - 1
O 4x² + 3x + 3
O 4x² + 2x + 11
g(x) = 3x - 2
h(x) = 4x² + 5
12121211.ooooooooooo
Pls answer will reward
The f(8) of the exponential function is 131072
How to find f(8) of the exponential function?
The general form of the exponential function is f(x) = abˣ
First, derive the function using the table. That is:
From the table, when x = 0, f(x) = 2. Substitute the values into the function:
f(x) = abˣ
2 = ab⁰ (Note: b⁰ = 1)
2 = a(1)
2 = a
a = 2
Also, from the table, when x = 3, f(x) = 128. Substitute the values into the function:
128 = 2 × b³
128 = 2b³
64 = b³
b³ = 64
b = ∛64
b = 4
We can now write the exponential function for the data:
f(x) = abˣ
f(x) = 2(4)ˣ
Thus, f(8) = 2(4)⁸ = 131072
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7.____________________means the number is divisible `by the number one and itself (it has exactly two factors only).
Prime Number means the number is divisible by the number one and itself (it has exactly two factors only).
What are Prime Numbers?
Natural numbers called prime numbers can only be divided by the number itself and by number 1. Alternatively stated, prime numbers are positive integers higher than one that have exactly two factors, 1, and the number itself.These are the first ten prime numbers: 2. 3. 5. 7. 11. 13. 17. 19. 23. 29.The number 1 neither qualifies as a prime nor a composite. With the exception of 2, which is both the smallest prime number and the only even prime number, all prime numbers are odd numbers.Every number over 1 can be divided by at least one prime, and even positive integers over two can be written as the sum of two primes.To learn more about Prime Numbers from the given link
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75 POINTS AND BRAINLIEST WILL BE GIVEN! FAKE ANSWERS WILL BE DELETED
Suppose O is a randomly chosen point inside triangle ABC. Line segments DE, FG, and HI are drawn through point O such that DE is parallel to AB, FG is parallel to BC, and HI is parallel to AC. The areas of triangle FOH, EOI, and GOD are equal to a, b, and c, respectively. Find the area of triangle ABC in terms of a, b, and c.
Answer:
A = (√a +√b +√c)²
Step-by-step explanation:
Given triangle ABC has interior point O that defined three similar triangles whose bases are the sides of triangle ABC and whose sides are lines through O parallel to the other two sides, and that those similar triangles have areas of 'a', 'b', and 'c', you want the area of ∆ABC in terms of 'a', 'b', and 'c'.
Scale factorsLet a reference to "triangle x" be a reference to "the triangle whose area is x", where x ∈ {a, b, c}. Let kx represent the ratio of the height of triangle x to the height of ∆ABC from the same base. If A is the area of ∆ABC, then ...
a/A = ka²b/A = kb²c/A = kc²The nature of point O is such that ka +kb +kc = 1.
This means ...
√(a/A) +√(b/A) +√(c/A) = 1
√a +√b +√c = √A . . . . . . . . . . multiply by √A
A = (√a +√b +√c)² . . . . . . . . . . square both sides
Need help ASAP please
Please find attached the drawing of the segment IK, the angle bisector of angle ∠HIJ that measures 52°, created with MS Word
What is an angle bisector?An angle bisector is a line or segment that divides an angle into two congruent angles.
The steps to construct an angle bisector are as follows;
With the indicated angle in the question, place the compass needle at the vertex, I, then draw an arc that intersects the rays that form the anglePlace the pointer at one of the intersection of the arc and the ray IJ that form the angle, and with a suitable compass openine, draw an arc in the interior region of the anglePlace the compass pointer at the second point of intersection of the arc from step one and the ray IH and with the same radius used in step 2, draw a second arc to intersect the first one and label the point KDraw a line joining K to I The segment IK is the angle bisector of the angle ∠HIJLearn more on geometric construction here: https://brainly.com/question/28568076
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Please help me im struggling so much in this!
1. The probability that the student is a male who earned an A is 9 / 19.
2. The probability that the student is a female who earned a C is 4 / 21.
3. The probability that the student is a male is 38 / 59.
4. The probability that the student earned a B is 29 / 59.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
1. The probability that the student is a male who earned an A is given as,
P = 18 / 38
P = 9 / 19
2. The probability that the student is a female who earned a C is given as,
P = 4 / 21
3. The probability that the student is a male is given as,
P = 38 / 59
4. The probability that the student earned a B is given as,
P = 29 / 59
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MATH PROLBEM FOR 53 POINTS
If EC = 13, and AD = 10, find DC.
The length of DC is 24.
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
Given is a figure of a quadrilateral.
Given that EC = 13.
Then AE = 13, since the diagonals bisect each other.
AC = 13 + 13 = 26
AD = 10
Using Pythagoras Theorem,
(AC)² = (AD)² + (DC)²
26² = 10² + (DC)²
(DC)² = 26² - 10²
= 576
DC = √576 = 24
Hence the length of the side DC is 24,.
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I NEED THE ANSWER ASAP
If you were to write the slope-intercept equation for a line that goes through the point (4,-3)--with a slope of -2--what would be the value of b?
y=mx+b
Question answer options:
b = 5
b = 11
b = -5
b = -11
Answer: b= 5
Step-by-step explanation:
y + 3 = -2(x-4)
y = -2x + 8 -3
y = -2x + 5
b = 5
Please help me with the following question.
The probability that her total wait time over the course of 60 das is less than 5.5 hour is a. 0.426.
What is Normal Probability Distribution?Problems of normal distributions can be solved using the z-score formula.
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 p-value, we get the probability that the value of the measure is greater than X.
In a set with mean and standard deviation , the z-score of a measure X is given by:
Z = (X - μ)/ σ
The mean μ= 6
The standard deviation σ = √12
For n instances of a normal variable, 60 days, for each day, mean 6, variance of 12.
So,
z = 330 - 360/720
z = 1.12
P(Z <-1.12) = 0.426
Thus, the correct answer is given by option A 0.426.
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