if you draw a random sample of 1,000 observations, what is the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24?

Answer:

95°

Step-by-step explanation:

X is the same of H that is you answer

To prove the existence of a subspace U ⊆ V such that U ∩ ker(T) = {0} and im(T) = {T(u) : u ∈ U}, we can construct such a subspace U as follows:

1. Let {v_1, v_2, ..., v_n} be a basis for ker(T), where n is the dimension of ker(T). Since V is finite dimensional, we can extend this set to a basis {v_1, v_2, ..., v_n, u_1, u_2, ..., u_m} for V, where m is the dimension of V.

2. Define U as the subspace spanned by the vectors {u_1, u_2, ..., u_m}. In other words, U = span{u_1, u_2, ..., u_m}.

Now, let's prove the desired properties of U:

(a) U ∩ ker(T) = {0}:

Assume there exists a non-zero vector x ∈ U ∩ ker(T). Then x can be written as a linear combination of the vectors {u_1, u_2, ..., u_m}:

x = a_1u_1 + a_2u_2 + ... + a_mu_m,

where a_1, a_2, ..., a_m are scalars. Since x is also in ker(T), we have T(x) = 0. Using linearity of T, we get:

T(x) = T(a_1u_1 + a_2u_2 + ... + a_mu_m) = a_1T(u_1) + a_2T(u_2) + ... + a_mT(u_m) = 0.

Since {u_1, u_2, ..., u_m} is linearly independent, the only way for the above equation to hold is if a_1 = a_2 = ... = a_m = 0. Therefore, x = 0, which shows that U ∩ ker(T) = {0}.

(b) im(T) = {T(u) : u ∈ U}:

Since U = span{u_1, u_2, ..., u_m}, any vector u ∈ U can be written as a linear combination of the vectors {u_1, u_2, ..., u_m}:

u = b_1u_1 + b_2u_2 + ... + b_mu_m,

where b_1, b_2, ..., b_m are scalars.

Now, let's consider T(u):

T(u) = T(b_1u_1 + b_2u_2 + ... + b_mu_m) = b_1T(u_1) + b_2T(u_2) + ... + b_mT(u_m).

Since T(u_1) = 0 (because u_1 ∈ ker(T)) and T(u_i) ∈ im(T) for i = 2 to m, we have:

T(u) = b_2T(u_2) + ... + b_mT(u_m) ∈ im(T).

Therefore, im(T) = {T(u) : u ∈ U}.

By constructing the subspace U as described above, we have shown that there exists a subspace U ⊆ V such that U ∩ ker(T) = {0} and im(T) = {T(u) : u ∈ U}.

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Answer:

52

52

is the correct answer the probability that card drawn is a faace card

Answer:

the probability of a drawing club is 13/52.

The probability of drawing a face card is 12/52.

Step-by-step explanation:

hope it's helpful

Answer:

D.  combining like terms

Step-by-step explanation:

You are combining like terms by adding 5 and 9 together.

The set G = {A, B} does not form a group under matrix multiplication.

In order for a set to form a group under matrix multiplication, it must satisfy certain criteria, such as closure, associativity, identity element, and inverse elements. In this case, the set G = {A, B} does not form a group because it fails to satisfy closure. Matrix multiplication is not closed under this set, meaning that the product of matrices A and B is not in the set G.

To transform the set G into a group, we need to add matrices that ensure closure, associativity, an identity element, and inverse elements. By adding a minimum number of matrices to the set G, we can create a group.

Regarding the second part of the question, we need to determine whether the group G formed in part 5a is isomorphic to the group K = {1, -1, i, -i} with respect to multiplication. Isomorphism refers to a bijective mapping between two groups that preserves the group structure. To determine if G and K are isomorphic, we need to examine their respective properties, such as the operation, closure, associativity, identity element, and inverses. By analyzing these properties, we can establish whether G and K are isomorphic or not.

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The Total surface of triangular prism  is 112 inches.

To calculate the surface area of a triangular prism, you need the measurements of the base and the height of the triangular faces, as well as the length of the prism.

The given measurements are;

Base ; 5 inches and  4 inches

height is 8 inches

Length of the prism is 2 inches.

To find the total surface area, we sum up the areas of all the faces:

Total surface area = area of triangular  faces + area of rectangular faces + area of lateral faces.

area of triangular faces = 5 inches × 4 inches = 20 inches.

area of the two faces = 20 ×2 =40

Area rectangular faces = 5 inches × 8 inches/ 2 = 40 inches.

Area of lateral faces = 8 inches ×2 = 16 square inches

for the two lateral faces is 16 × 2 = 32 square inches.

Total surface area = 40 square inches + 40 inches + 32 square inches = 112 square inches.

The Total surface of triangular prism  is 112 inches.

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This equation represents a quadratic polynomial with x-intercepts at -2 and 2, and a y-intercept at (0, 4). Note that there may be other valid equations for polynomials with the same long-run behavior, but this is one possible answer.

To find an equation for a polynomial with the given long-run behavior and points, we can start by considering the x-intercepts at -2 and 2, and the y-intercept at (0, 4). Let's proceed step by step:

1. Since the polynomial has x-intercepts at -2 and 2, we know that the factors (x + 2) and (x - 2) must be present in the equation.

2. We also know that the y-intercept is at (0, 4), which means that when x = 0, the polynomial evaluates to 4. This gives us an additional point on the graph.

3. To find the degree of the polynomial, we count the number of x-intercepts. In this case, there are two x-intercepts at -2 and 2, so the degree of the polynomial is 2.

Putting it all together, the equation for the polynomial can be written as:

f(x) = a(x + 2)(x - 2)

Now, we need to find the value of the coefficient 'a'. To do this, we substitute the y-intercept point (0, 4) into the equation:

4 = a(0 + 2)(0 - 2)

4 = a(-2)(-2)

4 = 4a

Dividing both sides by 4, we find:

a = 1

Therefore, the equation for the polynomial with the given long-run behavior and points is:

f(x) = (x + 2)(x - 2)

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Answer:

2 million

Step-by-step explanation:

In 41 years the population will be 1 million. In another 41 million, if the population continues to double, it will be double 1 million, which is equivalent to 2 million.

12. MATLAB code: `f = (-3*t.^2 + 5*t + 20).*(t < 0) + (3*t.^2 + 5*t).*(t >= 0)`

13. MATLAB function: `function random_values = UniGen(n, a, b); random_values = (b - a) * rand(n, 1) + a; end`

MATLAB code to calculate f(t) using the given equation:

t = -9:0.5:9; % Generate values of t from -9 to 9 in steps of 0.5

f = zeros(size(t)); % Initialize f(t) vector

for i = 1:numel(t)

   if t(i) < 0

       f(i) = -3*t(i)^2 + 5*t(i) + 20;

   else

       f(i) = 3*t(i)^2 + 5*t(i);

   end

end

% Display the results

disp('t    f(t)');

disp('--------');

disp([t' f']);

```

This code generates values of `t` from -9 to 9 in steps of 0.5 and calculates `f(t)` based on the given equation. The results are displayed in a tabular format showing the corresponding values of `t` and `f(t)`.

13. MATLAB function UniGen to generate uniformly distributed random values:

function random_values = UniGen(n, a, b)

   % n: Number of random values to generate

   % a: Start of the interval

   % b: End of the interval

   random_values = (b - a) * rand(n, 1) + a;

end

This MATLAB function named `UniGen` generates `n` random values that are uniformly distributed on the interval `[a, b]`. It utilizes the `rand` function to generate random values between 0 and 1, which are then scaled and shifted to fit within the specified interval `[a, b]`. The generated random values are returned as a column vector.

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4.571 billion years is equals to  1.4415 × 10⁷ seconds.

To calculate the number of seconds in 4.571 billion years, we first need to determine how many seconds there are in a year. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year. Multiplying these together gives us 31,536,000 seconds in a year.

Next, we multiply the number of seconds in a year by the number of years in 4.571 billion years. This gives us:

31,536,000 seconds/year x 4,571,000,000 years = 1.4415 × 10¹⁷ seconds

Therefore, there are approximately  1.4415 × 10¹⁷ seconds  in 4.571 billion years.

It's worth noting that this calculation assumes a standard year of 365 days. In reality, a year is slightly longer than 365 days, and so the actual number of seconds in 4.571 billion years would be slightly higher. Nonetheless, this calculation provides a good approximation.

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Check the picture below.

The net electric field of particle 1 and particle 2 will be zero at a coordinate on the x-axis that is a multiple of L/8.

The net electric field at a point on the x-axis due to particle 1 and particle 2 can be calculated using Coulomb's law:

Electric field due to particle 1: E1 = kq1/\(r1^{2}\)

Electric field due to particle 2: E2 = kq2/\(r2^{2}\)

Here, k is the electrostatic constant, q1 and q2 are the charges of particle

1 and particle 2 respectively, and r1 and r2 are the distances from the particles to the point on the x-axis.

To find the coordinate on the x-axis where the net electric field is zero, we need the magnitudes of E1 and E2 to be equal. Taking the magnitudes of the electric fields:

|E1| = |E2|

Using the expressions for E1 and E2:

k*|q1|/\(r1^{2}\) = k*|q2|/\(r2^2\)

Since the charges q1 and q2 are given as -4.90q and +3.70q respectively, and the magnitudes are equal:

(4.90q)/r = \(r1^2\)3.70q)/\(r2^2\)

Simplifying, we get:

\(r2^2\)/\(r1^2\) = 4.90/3.70

Taking the square root of both sides:

r2/r1 = \(\sqrt{(4.90/3.70)}\)

r2/r1 = sqrt\(\sqrt{(1.324)}\)

r2/r1 ≈ 1.150

Thus, the ratio of distances r2/r1 is approximately 1.150.

Since the particles are fixed to the x-axis, the distance between them is L, and the ratio r2/r1 is L/x, where x is the coordinate we are looking for.

Therefore, we have:

L/x ≈ 1.150

Solving for x, we find:

x ≈ L/1.150

Hence, the coordinate on the x-axis where the net electric field of the particles is zero is approximately L/1.150, or equivalently, a multiple of L/8.

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Answer:

number is 7

Step-by-step explanation:

let n be the number then 6 times the number is 6n and 5 added to it is

6n + 5 = 47 ( subtract 5 from both sides )

6n = 42 ( divide both sides by 6 )

n = 7

the required number is 7

The lateral surface area pentagonal prism is the perimeter of the base of the prism multiplied by its height. While the total area of a pentagonal prism is the sum of the areas of its two bases and its lateral surface area.

LSA= 5b * h

Where,

LSA = lateral surface area of a pentagonal prism,

b =  base of the prism

h =  height  of the prism

the pentagTSA= 5ab + 5bh

where,

The total surface area of the pentagonal prism, TSA

a=apothem length of the pentagonal prism

b= base length of the pentagonal prism

h= height of the pentagonal prism

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Answer:Mode = 33, Mean = 35.5

Step-by-step explanation:

The mode is whatever number appears the most.

To find the mode, first put the numbers in order from least to greatest.

29, 31, 33, 33, 37, 38, 40, 43

In this case, 33 appears the most, so the mode is 33.

The mean is the average of all of the numbers.

Firstly, add up all of the numbers:

29 + 31 + 33 + 33 + 37 + 38 + 40 + 43 = 284

Now that you have all of them added up, divide the final sum by the number of numbers you have in the list. In this case, you have 8 numbers.

284/8 = 35.5

Your mean is 35.5

Answer:

28+12x

Step-by-step explanation:

Multiply 7 with 4

Multiply 3x with 4

Answer:

28+12x

im pretty sure that is right

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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The type of sampling that requires giving every part an equal chance of being selected for the sample is called "simple random sampling."

Simple random sampling is a method of selecting a sample from a population where each member has an equal probability of being chosen. In this type of sampling, every part or element of the population is assigned a number or label, and a random process, such as a lottery or a random number generator, is used to select the sample. The main characteristic of simple random sampling is that each member of the population has an equal and independent chance of being selected, without any bias or preference.

This sampling method ensures that every part of the population has an equal opportunity to be included in the sample, making it a fair representation of the entire population. By giving each part an equal chance of being selected, simple random sampling helps to minimize sampling errors and increase the generalizability of the findings to the larger population. It is often used in research studies and surveys when the goal is to obtain an unbiased and representative sample.

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Answer:

-5 is the y intercept.

Step-by-step explanation:

Ok, lets do the steps in order.

1) Make a point-slope form equation.

We know that the format of it is y - y1 = slope(x - x1), so we know have to substitute our information in the equation.

y - 5 = 5(x - 2)

2) Convert our point-slope form equation into slope intercept form, and solve for the y-intercept.

y = slope(x) + b... right? So we now have to do math.

Distribute the right side of the equation to get :

y - 5 = 5x - 10

Now cancel out the -5, and then subtract on both sides.

y = 5x - 5

And -5 is your y intercept :)

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The integral {=°* (24 – 7) 4dx, evaluated with the substitution u = x4 – 7, is equal to (17/3) (x4 – 7)^(-3/4) + C, where C is the constant of integration.

To evaluate the integral {=°* (24 – 7) 4dx, we can first make the substitution u = x4 – 7. This means that du/dx = 4x3, or dx = du/(4x3).

Substituting these into the original integral, we get: {=°* (24 – 7) 4dx = {=°* (24 – 7) 4(du/(4x3)) Simplifying, we can cancel out the 4s and get: {=°* (24 – 7) 4dx = {=°* (24 – 7)/x3 du Now we can integrate with respect to u: {=°* (24 – 7)/x3 du = {=°* (17/u) du

Substituting back in for u, we get: {=°* (17/u) du = {=°* (17/(x4 – 7)) du To find the anti derivative of this, we can use the power rule of integration, which says that: ∫ x^n dx = (x^(n+1))/(n+1) + C Applying this to our integral, we get: {=°* (17/(x4 – 7)) du = 17 ∫ (x4 – 7)^(-1) dx

Using the power rule, we can integrate to get: 17 ∫ (x4 – 7)^(-1) dx = 17 * (1/3) (x4 – 7)^(-3/4) + C Finally, we substitute back in for u, which gives: 17 * (1/3) (x4 – 7)^(-3/4) + C = (17/3) (x4 – 7)^(-3/4) + C

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The altitude of Polaris, also known as the North Star, refers to its angle above the horizon when observed from a specific location on Earth.

The altitude of Polaris varies depending on the observer's latitude.

For an observer at the North Pole (latitude 90 degrees), Polaris appears directly overhead, at an altitude of 90 degrees. This means Polaris is at the zenith, the highest point in the sky.

For observers at other latitudes in the Northern Hemisphere, Polaris will appear lower in the sky. The altitude of Polaris is equal to the observer's latitude. For example, if you are at a latitude of 40 degrees north, Polaris will have an altitude of approximately 40 degrees above the horizon.

It's important to note that the altitude of Polaris remains relatively constant throughout the night and throughout the year due to its proximity to the celestial north pole. This makes it a useful navigational reference point for determining direction and latitude in the Northern Hemisphere.

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Answer:

number of people=4+1

=5

144/5=28.5

28×5=140

Step-by-step explanation:

how many pencils will be left over?=144-140

=4

After sharing 144 pencils equally among 5 people they left with 4 pencils.

Given that, Terry has a box of 144 colored pencils.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Terry and 4 of his friends share the pencils equally

So, including terry there are 5 people

Here,

5|144|28

  10
______

    44
    40
______
      4

Each of the them get 28 pencils, after sharing equally, they left with 4 pencils

Therefore, after sharing 144 pencils equally among 5 people they left with 4 pencils.

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The equation for the curve in terms of sin(θ) and cos(θ) is 4cos(θ) = 8sin(θ), the curve described by the given equation is a line.

The given equation, \(r^2cos(2\theta) = 64\), can be rewritten in terms of sin(θ) and cos(θ) using trigonometric identities.

By substituting\(r^2 = 4(cos^2(\theta) + sin^2(\theta))\) and\(cos(2\theta) = cos^2(\theta) - sin^2(\theta)\), we can simplify the equation to 4cos(θ) = 8sin(θ).

To find the Cartesian equation for the curve, we can convert the polar equation to rectangular coordinates.

Using the relationship between polar and rectangular coordinates (x = rcos(θ), y = rsin(θ)), we substitute \(r^2 = x^2 + y^2\) and rewrite the equation as 4x = 8y. This equation represents a line.

Therefore, the curve described by the given equation is a line.

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Answer: Since 2005 the amount of money spent on restaurants in a certain country has increased at a rate of 4% each year. In 2005, about 670 billion was spent on restaurants.

To find the amount spent on restaurants in 2013, we can use the formula:

A = P(1 + r)^t

Where:

A = the final amount

P = the initial amount (670 billion)

r = the rate of increase (0.04 or 4%)

t = the number of years since the initial amount (8 years)

Plugging in the values, we get:

A = 670 billion (1 + 0.04)^8

A = 670 billion (1.04)^8

A = 670 billion * 1.4304

A = 951.8 billion

So, if the trend continues, about 951.8 billion will be spent on restaurants in 2013.

Step-by-step explanation:

Answer:

None of the given points satisfy the inequality 2x - 3y < 1.

Step-by-step explanation:

To determine which points satisfy the inequality 2x - 3y < 1, we can substitute the coordinates of each point into the inequality and check if the inequality holds true.

Let's consider the given points:

Point A: (1, 0)

2(1) - 3(0) < 1

2 - 0 < 1

2 < 1 (False)

Point B: (-1, -1)

2(-1) - 3(-1) < 1

-2 + 3 < 1

1 < 1 (False)

Point C: (3, -2)

2(3) - 3(-2) < 1

6 + 6 < 1

12 < 1 (False)

None of the given points satisfy the inequality 2x - 3y < 1.

Therefore, none of the points A, B, or C satisfy the inequality.

9514 1404 393

Answer:

  a = 1

Step-by-step explanation:

The altitude is perpendicular to line QR, so point Q lies on a line through R that is perpendicular to the given altitude line. The given altitude line has a slope of -1. This means line QR will have a slope of 1, so the line QR in point-slope form is ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y -4 = 1(x -3)

Since point Q(a, 2a) is on this line, its coordinates will satisfy this equation.

  2a -4 = a -3

  a = 1 . . . . . . . . add 4-a to both sides

_____

The line with slope 2 on the attached diagram is the locus of all possible points Q. The one of interest is the one that is on the perpendicular through R.

__

Additional comment

In order for a line to be an altitude to side QR, it must go through point P. The given line (y=-x+6) does not go through point P. We assume that the line y=-x+5 is the one that is intended.

The volume of a cinder cone volcano will be 110872040 cubic feet.​

The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.

The volume of the cone (V) = 1/3 πhr²

Given,

Radius of cone (r) = 1100/2 = 550 feet

Height of cone (h) = 350 feet

The volume of a cinder cone volcano = 1/3 πhr²

Substitute the values of h and r,

The volume of a cinder cone volcano = 1/3 × 3.14× (550)² × (350)

The volume of a cinder cone volcano = 110872040 cubic feet.​

Thus, the volume of a cinder cone volcano will be 110872040 cubic feet.​

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Both series converge to the function\(f(x) = x^2 / (1 - x^2)\)within their respective intervals of convergence (-1 < x < 1) This is a geometric series with a common ratio of \(x^2.\) For a geometric series to converge, the absolute value of the common ratio must be less than 1.

|\(x^2 | < 1\) Taking the square root of both sides: | x | < 1 So, the interval of convergence for this series is -1 < x < 1. To find the function to which the series converges, we can use the formula for the sum of an infinite geometric series: S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.

In this case, the first term a is 2 and the common ratio r is 2 (since it's a geometric series). So, the function to which the series converges within its interval of convergence is: \(S = x^2 / (1 - x^2).\)

The second series is \(x^2 + x^4 + x^6 + x^8 + ...\)

Similarly, for convergence, we need, which simplifies to | x | < 1. So, the interval of convergence for this series is -1 < x < 1. Using the formula for the sum of an infinite geometric series, we have: S = a / (1 - r),

where a is the first term and r is the common ratio. In this case, the first term a is \(x^2\) and the common ratio r is \(x^2.\)The function to which the series converges within its interval of convergence is:

\(S = x^2 / (1 - x^2).\)

Therefore, both series converge to the function\(f(x) = x^2 / (1 - x^2)\)within their respective intervals of convergence (-1 < x < 1).

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If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

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The 98% confidence interval for the number of chocolate chips per cookie in Big Chip cookies is approximately 13.5529 to 15.0471 chips.

To find the 98% confidence interval for the number of chocolate chips per cookie in Big Chip cookies, we'll use the t-distribution since the sample size is relatively small (n = 61) and we don't know the population standard deviation.

The formula for the confidence interval is:

\(CI = \bar X \pm t_{critical} \times \dfrac{s } {\sqrt{n}}\)

where:

X is the sample mean,

\(t_{critical\) is the critical value for the t-distribution corresponding to the desired confidence level (98% in this case),

s is the sample standard deviation,

n is the sample size.

First, let's find the critical value for the t-distribution at a 98% confidence level with (n-1) degrees of freedom (df = 61 - 1 = 60). You can use a t-table or a calculator to find this value. For a two-tailed 98% confidence level, the critical value is approximately 2.660.

Given data:

X (sample mean) = 14.3

s (sample standard deviation) = 2.2

n (sample size) = 61

\(t_{critical\) = 2.660 (from the t-distribution table)

Now, calculate the confidence interval:

\(CI = 14.3 \pm 2.660 \times \dfrac{2.2} { \sqrt{61}}\\CI = 14.3 \pm 2.660 \times \dfrac{2.2} { 7.8102}\\CI = 14.3 \pm 0.7471\)

Lower bound = 14.3 - 0.7471 ≈ 13.5529

Upper bound = 14.3 + 0.7471 ≈ 15.0471

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