A random sample of size n = 74 is taken from a population with mean ? =-14.1 and standard deviation ? = 6 Use Table 1 a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. (Negative values should be indicated by a minus sign. Round "expected value" to 1 decimal place and "standard error" to 4 decimal places.) Expected value _________
Standard error ________
b. What is the probability that the sample mean is less than -14? (Round "z" value to 2 decimal places and final answer to 4 decimal places.) Probability__________
c. What is the probability that the sample mean falls between -14 and -13? (Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to 4 decimal places.) Probability__________

The surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 24 meters is 1,670.5 square meters.

The surface area of a cone is calculated using the following formula:

Surface area = πr² + πrl, where π is approximately equal to 3.14, r is the radius of the base of the cone, and l is the slant height of the cone.

In this problem, we are given that the height of the cone is 42 meters and the diameter of the base is 24 meters. The radius of the base is half of the diameter, so the radius is 12 meters. The slant height of the cone can be calculated using the Pythagorean theorem.

l² = 12² + 42²

l² = 1764

l = 42.01 meters

The surface area of the cone is then calculated as follows:

Surface area = πr² + πrl

Surface area = 3.14 * 12² + 3.14 * 12 * 42.01

Surface area = 1,670.5 square meters

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Answer:

D

Step-by-step explanation:

40% = \(\frac{40}{100}\) = \(\frac{2}{5}\) ← in simplest form

Then

\(\frac{2}{5}\) of $120 = \(\frac{2}{5}\) × $120 = 2 × $24 = $48

she pays $120 - $48 = $72

a) Using the Composite Trapezoidal Method with four intervals, the value of the integral of f(x) = 2ex + 5x³ in the interval [2, 8] is approximately 1388.88. Using Four-point Gauss Quadrature Integration, the value of the integral is approximately 1390.28.

b) Comparing the results with the exact (analytical) integral is not possible without the exact analytical form of the integral. However, we can determine the accuracy by comparing the approximate values obtained from the methods. In this case, the Four-point Gauss Quadrature Integration method is more accurate, as it provides a closer approximation to the exact integral.

a) i) To apply the Composite Trapezoidal Method, we divide the interval [2, 8] into four equal subintervals: [2, 4], [4, 6], [6, 8]. The formula for approximating the integral is:

∫[a, b] f(x) dx ≈ h/2 [f(a) + 2Σf(xi) + f(b)]

where h is the step size (h = (b - a)/n), xi represents the intermediate points within each subinterval, and n is the number of intervals.

In this case, with four intervals (n = 4), the step size is h = (8 - 2)/4 = 1.5. Evaluating the function at the endpoints and intermediate points, we get:

f(2) = 2e² + 40

f(4) = 2e⁴ + 320

f(6) = 2e⁶ + 1080

f(8) = 2e⁸ + 2560

Plugging these values into the formula, we have:

∫[2, 8] f(x) dx ≈ (1.5/2)[f(2) + 2(f(4) + f(6)) + f(8)]

≈ (1.5/2)[(2e² + 40) + 2(2e⁴ + 320 + 2e⁶ + 1080) + (2e⁸ + 2560)]

≈ 1388.88

ii) Four-point Gauss Quadrature Integration is a numerical integration method that approximates the integral using a weighted sum of function values at specific points. The formula for this method is:

∫[-1, 1] f(x) dx ≈ (b - a)/2 Σwi f(xi)

where b and a are the upper and lower limits of integration, xi represents the specific points within the interval, and wi are the corresponding weights.

Applying this method to the interval [2, 8], we need to transform it to the interval [-1, 1] using a linear transformation: x = ((b - a)t + (a + b))/2.

Substituting the transformed values into the formula, we have:

∫[2, 8] f(x) dx ≈ (8 - 2)/2 Σwi f(xi)

≈ 6/2 Σwi f(xi)

Using the specific points and weights for the Four-point Gauss Quadrature method, we obtain:

∫[2, 8] f(x) dx ≈ (3/2)[f(-√(3/7)) + f(√(3/7)) + f(-√(3/5)) + f(√(3/5))]

≈ (3/2)[f(-0.774597) + f(0.774597) + f(-0.538469) + f(0.538469)]

≈ 1390.28

b) To compare the results with the exact integral, we would need the exact analytical form of the integral, which is not provided in the prompt. However, based on the approximate values obtained, we can see that the Four-point Gauss Quadrature Integration method provides a closer approximation to the exact integral compared to the Composite Trapezoidal Method. Hence, the Four-point Gauss Quadrature Integration method is more accurate in this case.

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A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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Answer: you can put it into addition form or multiplication just take the number from that place as the right amount of zeros behind it and you should be good so on 6 it could be 90 or if your suppose to be putting it in multiplication it would be 9x10

Step-by-step explanation:

Answer:

read below

Step-by-step explanation:

decomposed answ:

6. 9*10

7. 4*10

8. 89*10

9. 3*100

10. 7*1000

11. 37*100

decomposition:

12. 56*10

13. 43*100

14. 60*100

a7ah7unaunauaunaa7au a7una8na8un

Answer:

y = 4x - 11

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 4x - 7 ← is in slope- intercept form

with slope m = 4

• Parallel lines have equal slopes , then

y = 4x + c ← is the partial equation of the parallel line

to find c substitute (3, 1 ) into the partial equation

1 = 12 + c ⇒ c = 1 - 12 = - 11

y = 4x - 11 ← equation of parallel line

Therefore, one container can hold 20/9 tons of sugar.

To simplify this expression, we can convert the mixed number 3 3/5 to an improper fraction:

3 3/5 = (5*3 + 3)/5 = 18/5

So the expression becomes:

8 tons / (18/5) containers

To divide by a fraction, we can multiply by its reciprocal:

8 tons / (18/5) containers = 8 tons * (5/18) containers

Now we can simplify the expression and solve for the amount of sugar in one container:

8 tons * (5/18) containers = 40/18 tons/container = 20/9 tons/container

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Heather, age 12, lives in the same household as her mother, uncle, and grandmother. The mother can qualify to claim Heather as a dependent and takes precedence.

A dependent is an individual who is unable to support themselves financially and needs the support of another person or family. Dependents can be children under the age of 19 or full-time students under the age of 24 or adults who are unable to take care of themselves. Heather is 12 years old and does not support herself financially.

Therefore, her mother can qualify to claim Heather as a dependent since they live in the same household. The mother is responsible for providing a home for Heather, making sure she has food and clothing, and taking care of her. Heather's uncle and grandmother can also claim her as a dependent if they provide more than half of her financial support or pay for her expenses.

Heather's mother takes precedence over her uncle and grandmother in claiming Heather as a dependent. When more than one person is eligible to claim the same dependent, the person with the higher adjusted gross income (AGI) takes precedence.

Since Heather lives with her mother, her mother has the first right to claim her as a dependent.

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The main difference between independent and conditional probability lies in whether the occurrence of one event affects the probability of the other event. To test for independence, you can use the formula P(A and B) = P(A) * P(B).

Independent probability refers to the probability of one event occurring without being influenced by the occurrence or non-occurrence of another event. In other words, the probability of one event happening does not affect the probability of the other event happening.

Conditional probability, on the other hand, refers to the probability of an event occurring given that another event has already occurred. It takes into account the relationship between two events and how the occurrence of one event affects the probability of the other event.

To determine if two events, A and B, are independent or dependent, you can use the formula: P(A and B) = P(A) * P(B). If the product of the probabilities of events A and B is equal to the probability of both events occurring together, then the events are independent. If the product is not equal to the probability of both events occurring together, then the events are dependent.

In conclusion, the main difference between independent and conditional probability lies in whether the occurrence of one event affects the probability of the other event. To test for independence, you can use the formula P(A and B) = P(A) * P(B).

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The difference between independent and conditional probability lies in the relationship between two events. Independent probability refers to the occurrence of one event not affecting the probability of the other event. On the other hand, conditional probability refers to the probability of an event occurring given that another event has already occurred.

To determine if two events, A and B, are independent or dependent, you can use a numerical test called the product rule. The product rule states that if two events are independent, then the probability of both events occurring is equal to the product of their individual probabilities. Mathematically, this can be expressed as:
P(A and B) = P(A) * P(B)
To determine if two events are dependent, you can compare the actual probability of both events occurring together (P(A and B)) with the expected probability if the events were independent (P(A) * P(B)). If the actual probability is equal to the expected probability, the events are independent. If the actual probability is different from the expected probability, the events are dependent.
Let's consider an example to illustrate this concept. Suppose we have a deck of 52 playing cards, and we draw two cards without replacement. Event A is drawing a red card, and Event B is drawing a spade.

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The value of the expression 200% of of $25,000 is $50,000

From the question, we have the following parameters that can be used in our computation:

200% of $25,000

The above expression is a percentage expression and mathematically, can be expressed as

Value = 200% of $25,000

Express "of" as products

So, we have

Value = 200% of $25,000

Evaluate the products in the expression

So, we have the following

Value = $50,000

Hence, the solution of the expression 200% of of $25,000 is $50,000

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Total 816 triangles that can be formed using diagonals from a common vertex of a 21-gon.

In mathematics, a diagonal is a line joining two vertices of a polygon or solid whose vertices do not lie on the same edge. Diagonals are generally defined as oblique lines or slanted lines connecting the vertices of a shape. A diagonal is defined as a horizontal shape with sides/edges and corners. 

Solution of the given problem:

Firstly, choose 3 vertices of 21-gon which are not adjacent to each other.

Secondly, connect all three vertices to a common vertex.

Now, there are 18 vertices that are not adjacent to common vertex and there are now 18 diagonals that can be drawn to the common vertex up to these vertices.

To form a triangle using these diagonals, we need to choose 3 of these 18 vertices, this can be calculated using the binomial coefficient formula:

18 choose 3 = 18! / (3! * (18 - 3)!) = (18 * 17 * 16) / (3 * 2 * 1) = 816

Thus, total 816 triangles can be formed.

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Step-by-step explanation:

y-y1=m(x-x1)

y-7=4(x+8)

y-7=4x+32

4x-y=-39

Answer:

y = 4x + 39

Step-by-step explanation:

Let's take another point (x,y) on the line.

Slope (m) = change in y ÷ change in x

∴ m = \(\frac{y - 7}{x - -8} = 4\)

y = 4x + 32 + 7

y = 4x + 39

The value of the exact length of the curve is 4 units.

The equations of the curve:x = 1 + 3t², y = 4 + 2t³, 0 ≤ t ≤ 1.

We have to find the exact length of the curve.To find the length of the curve, we use the formula:∫₀¹ √[dx/dt² + dy/dt²] dt.

Firstly, we need to find dx/dt and dy/dt.

Differentiating x and y w.r.t. t we get,

dx/dt = 6t and dy/dt = 6t².

Now, using the formula:

∫₀¹ √[dx/dt² + dy/dt²] dt.∫₀¹ √[36t² + 36t⁴] dt.6∫₀¹ t² √[1 + t²] dt.

Let, t = tanθ then, dt = sec²θ dθ.

Now, when t = 0, θ = 0, and when t = 1, θ = π/4.∴

Length of the curve= 6∫₀¹ t² √[1 + t²] dt.= 6∫₀^π/4 tan²θ sec³θ

dθ= 6∫₀^π/4 sin²θ/cosθ (1/cos²θ)

dθ= 6∫₀^π/4 (sin²θ/cos³θ

) dθ= 6[(-cosθ/sinθ) - (1/3)(cos³θ/sinθ)]

from θ = 0 to π/4= 6[(1/3) + (1/3)]= 4 units.

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Answer:

a) = 27

b) = 5

Sure, I'd be happy to help you with these questions!

a) To calculate the total number of possible 6-digit security numbers, we can use the permutation formula:

nPr = n! / (n-r)!

where n is the total number of digits available (9) and r is the number of digits we are selecting (6).

So, the number of possible 6-digit security numbers without any restrictions is:

9P6 = 9! / (9-6)! = 9! / 3! = 9 x 8 x 7 x 6 x 5 x 4 = 60,480

Therefore, there are 60,480 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits.

b) If the first digit cannot be a one, we are left with 8 choices for the first digit (since we cannot use 1) and 8 choices for the second digit (since we have already used one digit). For the remaining 4 digits, we still have 7 choices for each digit, since we cannot repeat any digits.

Using the permutation formula again, the number of possible 6-digit security numbers with the first digit not being one is:

8 x 8 x 7 x 7 x 7 x 7 = 1,322,496

Therefore, there are 1,322,496 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the first digit is not one.

c) To create an odd number, the last digit must be an odd number, which means we have 5 choices for the last digit (1, 3, 5, 7, or 9). For the first digit, we cannot use 0 or 1, so we have 7 choices. For the remaining 4 digits, we still have 8 choices for each digit (since we can use any digit).

Using the permutation formula again, the number of possible 6-digit security numbers with the last digit being odd is:

7 x 8 x 8 x 8 x 8 x 5 = 7,1680

Therefore, there are 7,1680 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the last digit is odd.

d) To create a number greater than 300,000, the first digit must be 3, 4, 5, 6, 7, 8, or 9. If the first digit is 3, we have 7 choices for the first digit (3, 4, 5, 6, 7, 8, or 9). For the remaining 5 digits, we still have 8 choices for each digit.

If the first digit is not 3, we have 6 choices for the first digit (since we cannot use 1 or 2). For the remaining 5 digits, we still have 8 choices for each digit.

Using the permutation formula again, the number of possible 6-digit security numbers greater than 300,000 is:

7 x 8 x 8 x 8 x 8 x 8 + 6 x 8 x 8 x 8 x 8 x 8 = 2,526,720

Therefore, there are 2,526,720 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the number is greater than 300,000.

e) To create a number greater than 750,000, the first digit must be 8 or 9. If the first digit is 8, we have 2 choices for the first digit (8 or 9). For the remaining 5 digits, we still have 8 choices for each digit.

If the first digit is 9, we only have one choice for the first digit (9). For the remaining 5 digits, we still have 8 choices for each digit.

Using the permutation formula again, the number of possible 6-digit security numbers greater than 750,000 is:

2 x 8 x 8 x 8 x 8 x 8 + 1 x 8 x 8 x 8 x 8 x 8 = 262,144

Therefore, there are 262,144 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the number is greater than 750,000.

The solution is F(x,y,λ) = 4x² + y² - 2xy - λ(x+y-14) and the extremum value of f(x,y) subject to the given constraint is located at (x,y) = (1.87, 12.13) which is a minimum value.

f(x,y) = 4x^2 + y^2 - 2xy, x+y = 14

To find the extremum of the function f(x,y) subject to the given constraint, we need to use the method of Lagrange multipliers.

We have to solve the following equations:

∂f/∂x = λ * ∂g/∂x and ∂f/∂y = λ * ∂g/∂y, where g(x,y) = x + y - 14

and λ is a Lagrange multiplier.

∂f/∂x = 8x - 2y

= λ

∂g/∂x = 1

∂f/∂y = 2y - 2x

= λ

∂g/∂y = 1

Solving the above set of equations we get

8x - 2y = 2y - 2x

=> 10x = 4y

=> 5x = 2y and x + y = 14

Substituting the value of y in the second equation we get

x + 5x/2 = 14

=> 7.5x = 14

=> x = 14/7.5

=> x = 1.87and y = 14 - x

=> y = 14 - 1.87

=> y = 12.13

The extremum value is located at (x,y) = (1.87, 12.13).

To find whether the above value is the maximum or minimum, we need to use the second derivative test.

Let D = ∂²f/∂x² * ∂²f/∂y² - (∂²f/∂x∂y)²

∂²f/∂x² = 8 and ∂²f/∂y² = 2, ∂²f/∂x∂y = -2

Therefore D = 8 * 2 - (-2)²= 16 > 0

∴ we have a minimum value at (x,y) = (1.87, 12.13).

Hence the solution is F(x,y,λ) = 4x² + y² - 2xy - λ(x+y-14) and the extremum value of f(x,y) subject to the given constraint is located at (x,y) = (1.87, 12.13) which is a minimum value.

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Answer:

14

Step-by-step explanation:

Answer:

D: {2, 3, 5, 8, 10}

R: {0, 1, 3, 5, 7}

Explanation:

The domain of a relation is the set of all input values (x-values) that will make the relation true.

Looking at the given table, we can see that the domain of the relation is as stated below;

D: {0, 1, 3, 5, 7}

The range of a relation is the set of all output values (y-values) that will make the relation true.

Looking at the given table, we can see that the range of the relation is as stated below;

R: {2, 3, 5, 8, 10}

Note that the domain of a relation is the same as the range of the inverse of the relation. Therefore, the domain of the inverse relation is as stated below;

D: {2, 3, 5, 8, 10}

Note also that range of a relation is the same as the domain of the inverse of the relation. Therefore, the range of the inverse relation is as stated below;

R: {0, 1, 3, 5, 7}

Answer:

2.15 ounces

Step-by-step explanation:

The total ounces of nuts in the bag is calculated as:

20 ounces of walnuts + 11.1 ounces of almonds + 24.8 ounces of cashews = 55.9 ounces.

From the question we are told that these amounts make 26 bags.

The number of ounces that are in each bag is calculated as:

26 bags = 55.9 ounces

1 bag = x ounces

Cross Multiply

26 bags × x ounces = 1 bag × 55.9 ounces

x ounces = 1 bag × 55.9 ounces/26 bags

x ounces = 2.15 ounces

Therefore, there are 1.94 ounces in each bag

The value of a will be -5.

Slope of a line is the measure of the steepness and the direction of the line.

Given that, the line that passes through (10, a) and (-2, -8) has a slope of value of 1/4.

Slope = (y2 - y1)/(x2 - x1)

1/4 = (-8-a)/(-2-10)

1/4 = (8+a)/12

8+a = 3

a = -5

Hence, The value of a will be -5.

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a. Null hypothesis (H0): μ1 = μ2 and Alternative hypothesis (H1): μ1 < μ2. b. The test statistic is -2.57 and p-value is  0.005 for the hypothesis test. c. At α = 0.05 it can be concluded that CPAs in states with flat state income tax rates work fewer hours per week during tax season compared to the average U.S. CPAs.

a. First, let's formulate the hypotheses:

Null hypothesis (H0): μ1 = μ2, which means that the mean hours worked per week during tax season by CPAs in states with flat state income tax rates is equal to the mean hours worked per week by all U.S. CPAs during tax season.

Alternative hypothesis (H1): μ1 < μ2, which means that the mean hours worked per week during tax season by CPAs in states with flat state income tax rates is less than the mean hours worked per week by all U.S. CPAs during tax season.

b. Now, let's compute the test statistic and p-value using the given sample data:

Sample mean (x) = 55 hours

Population mean (μ) = 60 hours

Population standard deviation (σ) = 27.4 hours

Sample size (n) = 150

We'll use the z-test for this hypothesis test:

z = (x - μ) / (σ / √n) = (55 - 60) / (27.4 / √150) ≈ -2.57

To find the p-value, we need to look up the z-value in the standard normal table, which gives us a p-value of approximately 0.005.

c. Lastly, let's draw our conclusion using α = 0.05:

Since the p-value (0.005) is less than α (0.05), we reject the null hypothesis (H0). This suggests that CPAs in states with flat state income tax rates work fewer hours per week during tax season compared to the average U.S. CPAs.

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margin of error = z* * sqrt(pq/n) = 1.55 * sqrt(0.150.85/280) ≈ 0.056

Rounded to 3 decimals, the margin of error is 0.056.

The 88% confidence interval for the percent of men in the general population who are color blind is:

p ± margin of error = 0.15 ± 0.056

Lower Bound: 0.15 - 0.056 = 0.094

Upper Bound: 0.15 + 0.056 = 0.206

Rounded to 3 decimals, the 88% confidence interval is (0.094, 0.206).

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Answer:

Answer:

Step-by-step explanation:

Answer:

all

Step-by-step explanation:

2x3=6 3x3=9 so 6:9

2x4=8 3x4=12 so 8:12

2x2=4 3x2=6 so 4:6

Answer:

50°

Step-by-step explanation:

Angles in a triangle always add up to 180°.

The square (bottom left of triangle) is a right angle and right angles always equal 90° and the other one is 40°, so you would add them up. This equals 130°.

To find y, you would have to do 180° minus 130° which is 50°.

Hope this helps :)

Answer:

They have already won 12 games so they need to win 15 more

Step-by-step explanation:

Hope it helps :)

Brainliest pls? Have a good day/night

The cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.

To find area of the composite figures,

The dimentions of the rectangle is 3 by 4 foot. The area of the rectangle is,

\(A_r=3\times4\\A_r=12\rm \;ft^2\)

The radius of the semicircle is 1.5 m. The area of the semicircle is,

\(A_{sc}=\dfrac{1}{2}\pi\times(1.5)^2\\A_{sc}=\dfrac{1}{2}(3.14)\times(1.5)^2\\A_{sc}=3.5325\rm\; ft^2\)

The area of the composite figure is,

\(A=12+3.5325\\A=15.5325\rm\;ft^2\\\)

The rate of  painting is $2.00 per square foot. Thus the cost to paint the figure is,

\(A=15.5325\times2\\A=31.065\)

Hence, the cost of painting the rectangular board with a semicircular top is $31.065 to the nearest hundredth.

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Answer:31

Step-by-step explanation:

Since the mean height of all children this age is 38 inches, the z-score is 1.282, and the child's height is 40 inches, the standard deviation of all children's heights will be 1561.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

Here,

The z-score which separates the top 10% of a normally distributed

population is 1.282.

Since z = (x-u)/sigma

1.282 = (40-38)/sigma

sigma = 2/1.282

sigma = 1/0.641 = 1561

The standard deviation of the heights of all children of this age will be 1561 as mean is 38 inch and z-score is 1.282 as well as the height of child is 40 inch.

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