How do you simplify this.

Answer:

the mean absolute deviation for the given data set is 1.86.

Step-by-step explanation:

To find the mean absolute deviation, we first need to find the mean of the data set.

Mean = (1.25 + 3.50 + 2.55 + 8.20 + 4.80 + 0.30 + 0.75 + 2.25) / 8 = 3.07

Next, we find the absolute deviation of each data point from the mean by subtracting the mean from each data point and taking the absolute value:

|1.25 - 3.07| = 1.82

|3.50 - 3.07| = 0.43

|2.55 - 3.07| = 0.52

|8.20 - 3.07| = 5.13

|4.80 - 3.07| = 1.73

|0.30 - 3.07| = 2.77

|0.75 - 3.07| = 2.32

|2.25 - 3.07| = 0.82

Then, we find the mean of these absolute deviations:

Mean absolute deviation = (1.82 + 0.43 + 0.52 + 5.13 + 1.73 + 2.77 + 2.32 + 0.82) / 8

Mean absolute deviation = 1.86

Therefore, the mean absolute deviation for the given data set is 1.86.

The probability that a student selected at random is a girl who chose apple as her favorite fruit is 0.32, or 32% rounded to the nearest hundredth.

To calculate the probability that a student is a girl who chose apple as her favorite fruit, we need to use the information provided in the table. First, we need to find the total number of girls who participated in the survey, which is the sum of the number of girls who chose apples, oranges, and mangoes as their favorite fruit, i.e., 46 + 41 + 55 = 142.

Next, we need to find the number of girls who chose apples as their favorite fruit, which is 46. Therefore, the probability that a student is a girl who chose apple as her favorite fruit is given by:

Probability = Number of girls who chose apples / Total number of girls in the survey

Probability = 46 / 142

Probability = 0.32

This means that out of all the girls who participated in the survey, 32% of them chose apple as their favorite fruit.

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Complete question is:

three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. this table lists the results.

               Boys Girls

Apple    66     46

Orange   52     41

Mango    40     55

if a survey is selected at random, what is the probability that the student is a girl who chose apple as her favorite fruit?

The 95% confidence interval for the mean filling weight of the cereal boxes is (1.300, 1.340) pounds.

To find the 95% confidence interval for the mean filling weight of the cereal boxes, we can use the formula

CI = x ± z × (σ/√n)

where:

x = sample mean filling weight = 1.32 pounds

σ = population standard deviation = 0.06 pounds

n = sample size = 43

z = z-score corresponding to the desired level of confidence (95% in this case)

To find the z-score, we can use a standard normal distribution table or calculator. For a 95% confidence level, the z-score is 1.96.

Plugging in the values, we get

CI = 1.32 ± 1.96×(0.06/√43)

CI = 1.32 ± 0.020

Therefore, the 95% confidence interval for the mean filling weight of the cereal boxes is (1.300, 1.340) pounds. This means that we can be 95% confident that the true population mean filling weight falls within this range.

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9. The value of the land today, if the land was purchased for $3,500 in 1960, at the value increased at 3% per year is $22,532.7

A percentage increase is the ratio of the difference in the initial and current value of an item to the initial value, expressed as a percentage.

The year the land was purchased = 1960

The amount at which the land was purchased, P = $3,500

The percentage rate by which the value of the land increased, r = 3%

The value of the land today, A, can be found using the compound interest formula as follows;

Value of the land, A = P·(1 + r)ⁿ

Where;

n = The number of years = 2023 - 1960 = 63

Therefore; A = 3500 × (1 + 3/100)⁶³ ≈ 22532.7

The value of the land today is about $22,532.7

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The area of the porch would be 7.5 square feet.

Now, let's move on to creating a grid for the porch in Aisha and Jordan's floor plan. The grid should have a scale, meaning each square on the grid should represent a certain measurement, such as one foot or one meter.

Next, you will need to shade the area of the porch on the grid. The porch in the floor plan is 1.25 ft by 6 ft, so on the grid, you can shade in 1.25 squares along the length of the porch and 6 squares along the width of the porch.

Finally, to find the area of the porch, you simply count the number of shaded squares on the grid. Each square on the grid represents a certain amount of area, based on the scale you established earlier.

If each square on the grid represents one square foot, and you shaded in 7.5 squares for the porch.

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Answer:

shade the grids to find the area of the porch.

The correct answer is C. 34.46.
This is because the area between the mean and a positive z score of 0.40 is 15.54%, which means the area between the mean and a negative z score of -0.40 is also 15.54%.

Therefore, the total area between the mean and a z score of -0.40 is the sum of the area to the left of the mean (which is 50%) and the area between the mean and a z score of -0.40 (which is 15.54%).

Total area between the mean and a z score of -0.40 = 50% + 15.54% = 65.54%.

To find the percentage of scores falling between the mean and a z score of -0.40, we subtract the area to the left of the z score from the total area between the mean and the z score:

Percentage of scores falling between the mean and a z score of -0.40 = Total area between the mean and a z score of -0.40 - Area to the left of the z score

= 65.54% - 50%

= 15.54%.

Therefore, the percentage of scores falling between the mean and a z score of -0.40 is 15.54%.

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The percentage of scores falling between the mean and a z score of –0.40 is also 15.54%. So the correct answer is B.

15.54.

This is because the normal distribution is symmetric around the mean, so the percentage of scores between the mean

and a positive z score is the same as the percentage of scores between the mean and the same negative z score.

This is because the area under the normal curve between a z score of 0.40 and –0.40 is symmetrical, meaning it is the

same on both sides of the mean.

Therefore, the percentage of scores falling between the mean and a z score of –0.40 is equal to the percentage of

scores falling between the mean and a z score of 0.40, which is 15.54%.

So the correct answer is B. 15.54.

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The solution set of an equation is the set of input values for which the equation is true.

The solution set of an equation is the set of all values of the variables that satisfy the equation. In other words, it is the set of all possible solutions that make the equation true.

For example, the solution set of the equation 2x - 4 = 0 is of {2}, as:

2x - 4 = 0

2x = 4

x = 4/2

x = 2.

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The remainder when  ƒ(x) = 2x³ – 3x – 2 is divided by x - 4 is 114.

To find the remainder when ƒ(x) is divided by (x - 4), we can use the remainder theorem, which states that the remainder when a polynomial ƒ(x) is divided by (x - a) is equal to ƒ(a).

So, we need to evaluate ƒ(4) to find the remainder when ƒ(x) is divided by (x - 4).

ƒ(x) = 2x³ – 3x – 2

ƒ(4) = 2(4)³ – 3(4) – 2

ƒ(4) = 2(64) – 12 – 2

ƒ(4) = 128 – 14

ƒ(4) = 114

Therefore, the remainder when ƒ(x) is divided by (x - 4) is 114.

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Answer:

6.8 ounces

To set up a hypothesis test for this production process, we need to define the null and alternative hypotheses. The null hypothesis (H0) is that the average amount of soda in each can is equal to 6.8 ounces, while the alternative hypothesis (Ha) is that the average amount of soda in each can is not equal to 6.8 ounces.

We can then collect data by taking regular random samples from the production process and calculate the sample mean and standard deviation. We can then perform a statistical test such as a t-test or z-test to determine whether we can reject or fail to reject the null hypothesis.

If we reject the null hypothesis, we can conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces. If we fail to reject the null hypothesis, we cannot conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces.

I hope this helps! Let me know if you have any other questions.

If the "lead-level" at  top is measured and from half, lead level at bottom is measured, then this will not be a valid matched pair test, because measurements of top and bottom should be from "same-glass", the correct options is (b).

A "Matched-Pair" test, also known as a paired or dependent samples test, is used when the data being compared comes from the same subjects or units that are matched or paired in some way.

In this case, the researcher is trying to compare lead levels between the top and bottom of a glass of water.

The measurements from the top and bottom of the glass are not from the same glass, as mentioned in the question.

So, it would not be valid to use a matched pair test in this scenario.

For a valid matched pair test, the measurements being compared should come from the same subjects or units that are matched or paired in some way to account for any potential confounding factors.

In this case, to accurately determine if lead levels are different between the top and bottom of a "glass-of-water", measurements should be taken from the same glass at both the top and bottom portions.

Therefore, Option(b) is correct.

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The given question is incomplete, the complete question is

A researcher wants to determine if lead levels are different between the top of a glass of water and the bottom of a glass of water. Many samples of water are taken. From half, the lead level at the top is measured and from half, the lead level at the bottom is measured.

Would this be a valid matched pair test?

(a) No, as the lead levels cannot be accurately measured,

(b) No, as the measurements of top and bottom should be from the same glass,

(c) Yes, as long as there are an equal number of glasses in each group,

(d) Yes, as long as they are all from the same faucet.

Answer: Let x be the measure of the smallest angle in the triangle. Then we have:

One angle is three times as large as another, so the second angle is 3x.

The third angle is 80° more than the smallest angle, so it is x + 80.

The sum of the angles in a triangle is always 180°, so we can write an equation:

x + 3x + (x + 80) = 180

Simplifying and solving for x, we get:

5x + 80 = 180

5x = 100

x = 20

Therefore, the smallest angle in the triangle is x = 20 degrees, the second angle is 3x = 60 degrees, and the third angle is x + 80 = 100 degrees.

Step-by-step explanation:

Sarah then purchased 9 coach seats as by increasing the first equation by 190 and deducting it from the second equation.

An equation is a logical statement that utilises the equal sign to demonstrate the equality of two expressions. Factors, constants, and mathematical like addition, reduction, multiply, division, and exponentiation can all be found in it. Equations are utilised to find solutions for problems in both mathematics and the real world.

given

Let's use the letters "c" for the quantity of coach tickets and "f" for the quantity of first-class tickets. We are aware that there were 12 travellers in all, so

c + f + 1 = 12

We also know that the entire cost of the airfare was $4650, with coach tickets costing $190 and first-class tickets costing $980. With this knowledge, we can construct the equation shown below:

[tex]190c + 980f = 4650 - 980[/tex]

When we simplify this equation, we obtain:

[tex]190c + 980f = 3670[/tex]

Elimination can now be used to find either "c" or "f." By increasing the first equation by 190 and deducting it from the second equation, let's get rid of "c":

[tex]190c + 190f + 190 = 2280[/tex]

-190c - 980f = -3670

-790f = -1390

f = 1.76

We can round "f" up to 2 because we cannot have a fractional number of persons.

c + 2 + 1 = 12

c = 9

Sarah then purchased 9 coach seats as by increasing the first equation by 190 and deducting it from the second equation.

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Answer:

Step-by-step explanation:

[tex]\sqrt{40}[/tex] = [tex]\sqrt{4}[/tex] x [tex]\sqrt{10}[/tex] = [tex]2\sqrt{10[/tex]

[tex]\frac{20}{2\sqrt{10} }[/tex] = [tex]\frac{10}{\sqrt{10} }[/tex]

[tex]\frac{10}{\sqrt{10} } * \frac{\sqrt{10} }{\sqrt{10} } = \frac{10\sqrt{10} }{10} = \sqrt{10} }[/tex]

[tex]\frac{1}{\sqrt{2} } = \frac{1}{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{\sqrt{2} }{2}[/tex]

From the above since [tex]\frac{20}{\sqrt{40} }[/tex]   is not equal to  [tex]\frac{1}{\sqrt{2} }[/tex] it implies that they are not the same

Answer:

The answer is B

The domain of the function is x≥ -2

Answer:

To do this you have to multiply 3.14 times the diameter, so 14 x 3.14 = 43.96 which is the diameter you cn round it!

Step-by-step explanation:

The volume of the rectangular prism is 1.6 cubic inches.

Let's start by finding the number of cubes that can fit in each dimension of the rectangular prism. Since each cube has an edge length of 1/5 inch, the length, width, and height of the rectangular prism must be multiples of 1/5 inch. Let's call the length of the rectangular prism "L", the width "W", and the height "H". Then we have

L = 1/5 × x

W = 1/5 × y

H = 1/5 × z

where x, y, and z are integers.

Since the rectangular prism is completely packed with 200 cubes, we have

x × y × z = 200

We want to find the volume of the rectangular prism, which is given by

V = L × W × H = 1/5 × x × 1/5 × y × 1/5 × z = 1/125 × x × y × z

Substituting x × y × z = 200, we get

V = 1/125 × 200 = 8/5 = 1.6 cubic inches

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The given question is incomplete, the complete question is:

A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. find the  volume of this rectangular prism

Answer: This triangle is isoscele

Step-by-step explanation:

The pair of required complementary angles are 26.2° and 63.8° respectively.

Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees.

When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.

If the total of two angles is 90o (ninety degrees), then the angles are complementary.

A 30-angle and a 60-angle, for instance, are two complementary angles.

So, to find the 2 angles which are complementary:

x + x + 37.6 = 90

Now, solve it as follows:

x + x + 37.6 = 90

2x = 90 - 37.6

2x = 52.4

x = 52.4/2

x = 26.2

Now, x = 26.2 and the second angle x + 37.6 is = 26.2 + 37.6 = 63.8°.

Therefore, the pair of required complementary angles are 26.2° and 63.8° respectively.

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Part A: The sample space is {A, E, R, S, T}. Part B: The favorable outcomes is 1/5 that is every card can appear. Part C: The probability of choosing two consonants is 6/20.

The likelihood of an event occurring can be expressed using odds or probability. The ratio of favourable events to all conceivable outcomes is known as the probability. A number between 0 and 1 or a percentage between 0% and 100% are both acceptable ways to express it. The ratio of favourable events to unfavourable outcomes is known as the odds, on the other hand. "Odds in favour" or "odds against" are two ways to express odds.

Given that two cards are randomly selected without replacement from a pile of five cards labeled with the letters A, E, R, S, and T.  

The probability of both cards being consonants are = 3 *2 = 6

Part A: The sample space is {A, E, R, S, T}.

Part B: The favorable outcomes is 1/5 that is every card can appear.

Part C: The consonants are R, S, T:

Thus, choosing 2 consonants the probability is:

3 x 2 = 6.

The total outcomes are: 5 * 4 = 20 ways

The probability of choosing two consonants is 6/20.

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The value of c in increasing order which satisfy the Rolle's theorem for a given function is equal to  c = 1/4 and c = 3/4.

Function f(x) = 7sin(2πx) ,

Interval = [0, 1]

To apply Rolle's Theorem, check the following conditions,

f(x) must be continuous on the closed interval [a, b].

Here, the interval is [0,1].

f(x) must be differentiable on the open interval (a, b).

f(a) = f(b)

Function f(x) = 7sin(2πx).

f(x) is continuous on the interval [0, 1].

f(x) is differentiable on the interval (0, 1), and its derivative is,

f'(x) = 14π cos(2πx)

The derivative is continuous on the interval (0, 1).

f(0) = 7sin(0)

     = 0

f(1) = 7sin(2π)

     = 0

Since f(0) = f(1) = 0,

⇒ As per Rolle's Theorem there exists at least one number c in the interval (0, 1) .

Such that f'(c) = 0.

Values of c that satisfy this conclusion,

Solve the equation

f'(c) = 14π cos(2πc)

⇒14π cos(2πc) = 0

⇒ cos(2πc) = 0

This equation has solutions at c = 1/4 and c = 3/4,

As

cos(2π(1/4))

= cos(π/2)

= 0

and

cos(2π(3/4))

= cos(3π/2)

= 0.

Therefore, the values of c that satisfy the conclusion of Rolle's Theorem for the given function are c = 1/4 and c = 3/4, and they are already in increasing order.

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The above question is incomplete, the complete question is:

Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function 7sin(2pix) and interval [0, 1 ]. Enter the values in increasing order and enter N in any blanks you don't need to use.

Answer:

A. .88 < 1, so the price of Fuel A is decreasing by 12% per month.

B. Fuel B, from months 1 to 4:

[tex] \frac{3.04 - 3.44}{3.44} (100\%) = - 11.63\%[/tex]

Over this four-month period, Fuel B's price has decreased by about 11.63%.

[tex] \sqrt[3]{1 - .1163} = \sqrt[3]{.8837} = .9596[/tex]

[tex]1 - .9596 = .0404 = 4.04\%[/tex]

So Fuel B's price has been decreasing by an average of about 4.04% per month. Fuel A recorded the higher percentage change in price per month.

Answer:

A trapezoid is defined as a quadrilateral with only 2 parallel sides. An

isosceles trapezoid is defined as a trapezoid with the non-parallel sides being

congruent. Prove that the base angles on an isosceles trapezoid ( are congruent

The relative frequency of the given students surveyed and prefer to go to Cook Middle School and Energy Flow is equal to 0.4 or 40%.

The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow

= (Number of students go to Cook Middle School and prefer Energy Flow) /( total number of students surveyed)

From the given table,

The number of students who go to Cook Middle School and prefer Energy Flow is  equal to 20.

The total number of students surveyed is equal to 50.

The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow is,

= 20/50

= 0.4

Therefore, the relative frequency of all students surveyed going to the Cook Middle School and prefer Energy Flow is equal to 0.4 or 40%.

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The above question is incomplete, the complete question is :

Some students at Cook Middle School and Elm Middle School participated in a survey. They were asked which sports drink they prefer: Gym Juice or Energy Flow. The two-way table shows the results.

                       Gym Juice        Energy Flow   Total

Cook                   15                     20                    35

Elm                       5                     10                     15

Total                    20                     30                     50

What is the relative frequency of all students surveyed who go to Cook Middle School and prefer Energy Flow?

The exponential function of the form y=ab^x that has the given points is y = 0.282 * (0.941)^x

We can use the two given points to form a system of equations to solve for the coefficients a and b in the exponential function y = ab^x.

Plugging in the first point (-16, 3/4), we get:

3/4 = ab^(-16)

Plugging in the second point (2, 1/4), we get:

1/4 = ab^2

Divide the equations

b^18 = 1/3

Taking the 18th root of both sides, we get:

b = (1/3)^(1/18)

b = 0.941

Since we need to find an exponential function that passes through both given points, we'll choose the positive value for b, which gives:

b = 0.941

Substituting this value of b into either equation to solve for a, we get:

1/4 = a(0.941)^2

a = 1/[4 * (0.941)^2]

a = 0.282

So, the exponential function that passes through the points (-16, 3/4) and (2, 1/4) is: y = 0.282 * (0.941)^x

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The exponential expression y = - 3 · (- 4 / 9)ˣ contains the points (- 1,6 + 3 / 4) and (2, 1 - 4).

In this question we must derive an exponential expression of the form y = a · bˣ, where a, b are real constants, that contains the points (- 1,6 + 3 / 4) and (2, 1 - 4). This equation can be found as the number of points equals the number of real constants. Then, we must solve the following system:

6.75 = a · b⁻¹

- 3 = a · b²

First, we find b by dividing the second equation by the first equation:

- 3 / 6.75 = b

b = - 4 / 9

Second, we determine the value of a:

a = 6.75 · b

a = 6.75 · (- 4 / 9)

a = - 3

Third, write the resulting exponential equation:

y = - 3 · (- 4 / 9)ˣ

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The values of "l" and "r" that maximize the area of the rectangular region are approximately 326.5 ft and 105.6 ft, respectively.

To find the values of "l" and "r" that maximize the area of the rectangular

region of the racetrack, we need to use optimization techniques.

Let's start by breaking down the rectangular region into its two

components: a rectangle and two semicircles.

Let "l" be the length of the rectangle and "r" be the radius of the

semicircles. Then we can express the area of the rectangular region as:

A = l(1056/5 - 2r)

the length of the track is 1056 ft, or 1/5 of a mile. Since there are two

semicircular ends, the length of the rectangle is equal to the length of

the track minus the combined length of the two semicircles, which is 2r.

To find the values of "l" and "r" that maximize the area of the rectangular

region, we need to find the critical points of the function A(l, r). To do this,

we can take partial derivatives of A with respect to both "l" and "r", and

set them equal to zerhttps://brainly.com/question/30883489o:

∂A/∂l = 1056/5 - 2r = 0

∂A/∂r = -2l + (2112/5 - 4πr) = 0

Solving the first equation for "r", we get:

r = 528/5

Substituting this value of "r" into the second equation and solving for "l", we get:

l = (2112/5 - 4πr)/2

l ≈ 326.5 ft (rounded to the nearest foot)

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The identity of the angles represent the type of angles in the question are;

7. ∠EJH, ∠IJH

8. ∠RVT, SVT, and ∠SVU, WVU, and ∠RVW, ∠UVW

9. ∠AED, ∠DEB

10. ∠JNM, ∠LNK

An angle is a geometric figure that indicates the amount of rotation obtained by the intersection of two lines that meet and share a common vertex point.

7. Complementary angles are angles that have a sum of 90° or form a right angle.

The complementary angles are ∠EJH and ∠IJH

8. Adjacent angles are two angles that are located side by side or next to each other, such that there share a common side or ray and a common vertex, without overlapping.

Adjacent angles includes; ∠RVT, and ∠SVT, ∠SVU and ∠WVU, ∠RVW, and ∠UVW

9. Supplementary angles are two angles that have a sum of 180°, or that form a straight line.

The supplementary angles includes; ∠AED, and ∠DEB

10. Vertical angles are angles formed by the intersection two straight lines, and which are located vertically opposite each other, and are always congruent. The vertical angles are; ∠JNM and ∠LNK

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Answer:

  2

Step-by-step explanation:

You want the average rate of change of f(x) = -x² -2x +6 on the interval [-7, 3].

The average rate of change of f(x) on the interval [a, b] is computed as ...

  m = (f(b) -f(a))/(b -a)

For the given function f(x), this is ...

  m = (f(3) -f(-7))/(3 -(-7)) = (-9 -(-29))/10 = 20/10 = 2

The average rate of change of f(x) on the interval [-7, 3] is 2.

__

Additional comment

The derivative of the function is f'(x) = -2x -2. The midpoint of the interval is x = (-7 +3)/2 = -2. The value of the derivative at the midpoint is equal to the average rate of change on the interval:

  -2(-2) -2 = 4 -2 = 2 . . . . average slope between x=-7 and x=3.

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The minimum score required for an A grade is approximately 87 when the standard deviation is 7.4 and the mean is 77.1

The standard deviation is a measure of the amount of variation or dispersion in a set of data. It measures how much the individual data points deviate or differ from the mean or average of the data set.

Mathematically, the standard deviation is the square root of the variance, which is calculated by taking the average of the squared differences of each data point from the mean. The formula for the standard deviation is:

σ = sqrt(Σ(x - μ)^2 / n)

where σ is the standard deviation, x is a data point, μ is the mean, and n is the number of data points.

First, we need to find the z-score corresponding to a score that is at the 92nd percentile (the top 8%). We can use the inverse normal distribution function (also known as the probit function) to do this:

invNorm(0.92) ≈ 1.41

This means that a score at the 92nd percentile corresponds to a z-score of approximately 1.41.

Next, we need to convert this z-score to a raw score on the test. We can do this using the formula:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

Rearranging this formula to solve for x, we get:

x = z*σ + μ

Substituting the values we have, we get:

x = 1.41*7.4 + 77.1 ≈ 87.4

Therefore, the minimum score required for an A grade is approximately 87, rounded to the nearest whole number.

To know more about the standard deviation visit:

brainly.com/question/13905583

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