Central limit theorem Imagine that you are doing an exhaustive study on the children in all of the elementary schools in your school district. You are particularly interested in how much time children spend doing active play on weekends. You find that for this population of 2,431 children, the average number of minutes spent doing active play on weekends is μ = 87.85, with a standard deviation of σ = 118.1. You select a random sample of 25 children of elementary school age in this same school district. In this sample, you find that the average number of minutes the children spend doing active play on weekends is M = 79.07, with a standard deviation of s = 129.91.The difference between M and 1.1 is due to the :_______

Answers

Answer 1

Answer:

Sampling error

Step-by-step explanation:

The answer is sampling error.

The sampling error occurs when the sample does not represent the full population and the result from the sample is not a representation of the results from full sample.

From information given

Population mean = 87.85

Population standard deviation = 118.1

n = 25

Sample mean = 79.07

Sample standard deviation = 129.91

118.2/√25

= 23.62

The standard deviation of the distribution is what is referred to as standard error of m = 23.62

Answer 2

Answer:

Final answer:

The difference between the population mean and sample mean is likely due to sampling variability, a concept related to the Central Limit Theorem. Given the small sample size in this case, it's not unusual to see this difference.

Explanation:

The difference between the mean of the population (μ) and the mean of the sample (M) is likely attributable to the phenomenon known as sampling variability. This is a concept central to the Central Limit Theorem, which states that when enough random samples are taken from a population, the distribution of the means of these samples will approximate a normal distribution, even if the original population distribution is not normal. The mean of this distribution will be equal to the populating mean, and its standard deviation will be the standard deviation of the population, divided by the square root of the sample size (n).

In this specific case, you've taken a relatively small sample (n=25) from a larger population (N=2,431). Consequently, it is not unexpected that there is some difference between the population mean (μ = 87.85) and the sample mean (M = 79.07). However, as you increase the number of samples you are drawing, according to the Central Limit Theorem, the average of these sample means should converge on the population mean.

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Evaluate ∫C ysin(z)ds, where C is the circular helix given by the equations x = cos(t), y = sin(t), z = t, 0 ≤ t ≤ 2π. SOLUTION The formula for a line integral in space gives the following. ∫y sin(z)ds = sin2(t) dt = (sin(t))2√ (cos(t))2 + (sin(t))2 + 1dt = 1 2 (1 - cos(2t))dt = √2 2 =

Answers

The line integral is

$\displaystyle\int_Cy\sin z\,\mathrm ds=\int_0^(2\pi)y(t)\sin z(t)\,\sqrt{\left((\mathrm dx)/(\mathrm dt)\right)^2+\left((\mathrm dy)/(\mathrm dt)\right)^2+\left((\mathrm dz)/(\mathrm dt)\right)^2}\,\mathrm dt$

We have

$x=\cos t\implies(\mathrm dx)/(\mathrm dt)=-\sin t$

$y=\sin t\implies(\mathrm dy)/(\mathrm dt)=\cos t$

$z=t\implies(\mathrm dz)/(\mathrm dt)=1$

so the integral reduces to

$\displaystyle\int_0^(2\pi)\sin^2t√((-\sin t)^2+\cos^2t+1^2)\,\mathrm dt=\frac{\sqrt2}2\int_0^(2\pi)(1-\cos2t)\,\mathrm dt=\boxed{\frac\pi{\sqrt2}}$

The line integral ∫C ysin(z) ds over the circular helix C, parametrized by x = cos(t), y = sin(t), z = t for 0 ≤ t ≤ 2π, evaluates to π√2.

To evaluate the line integral ∫C ysin(z) ds over the circular helix C given by x = cos(t), y = sin(t), z = t for 0 ≤ t ≤ 2π, we follow these steps:

1. Parameterize the curve: C is already parameterized as x = cos(t), y = sin(t), z = t.

2. Find the differential ds: ds = √(dx² + dy² + dz²) = √(sin²(t) + cos²(t) + 1)dt = √(1 + 1)dt = √2 dt.

3. Evaluate the integral: ∫C ysin(z) ds = ∫[0, 2π] sin(t) * sin(t) * √2 dt = ∫[0, 2π] sin²(t) * √2 dt.

Now, we'll integrate sin²(t) * √2 with respect to t:

∫ sin²(t) * √2 dt = (1/2) * ∫ (1 - cos(2t)) * √2 dt.

Using the power rule for integration, we get:

(1/2) * [(t - (1/2) * sin(2t)) * √2] | [0, 2π].

Plugging in the limits:

(1/2) * [(2π - (1/2) * sin(4π) - (0 - (1/2) * sin(0))) * √2].

Since sin(4π) = sin(0) = 0:

(1/2) * [(2π - 0 - 0) * √2] = π√2.

So, ∫C ysin(z) ds = π√2.

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Kai had a gross weekly paycheck of $616 last week. Kai worked 6 hours for 4 of the days and 8 hours on 1 day. What is Kai's hourly rate of pay? a. $16.21 b. $19.25 c. $20.53 d. $25.67 Please select the best answer from the choices provided

Answers

The correct answer is B. $ 19.25

Explanation:

To calculate the hourly rate of pay, first, let's calculate the total number of hours Kai worked, and then divide the total earned into the number of hours.

6 hours x 4 days = 24 hours

8 hours x 1 day = 8 hours

24 hours + 8 hours = 32 hours

This shows Kai worked a total of 32 hours. Now to find the hourly rate of pay, follow this procedure:

$616 (total earned) ÷ 32 hours = $19.25 each hour

This means Kai earns $19.25 for each hour of work and therefore the hourly rate of pay is $19.25.

Kai earns $19.25 for each hour of work that is the hourly rate of pay is $19.25. Hence option b is true.

Given that;

Kai had a gross weekly paycheck of $616 last week.

And, Kai worked 6 hours for 4 of the days and 8 hours on 1 day.

Now the total working hour would be,

The working hours in 4 days,

4 × 6 = 24 hours

The working hours in 1 day,

1 × 8 = 8 hours.

Hence, the total working hours in a week is,

24 + 8 = 32 hours

Since Kai had a gross weekly paycheck of $616 last week.

Hence, Kai's hourly rate of pay is,

$616 ÷ 32 = $19.25

Therefore, option b is true.

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A submarine at - 45 feet dives 50 feet. Write an expression to represent the submarine's elevation. Need help

Answers

-150+(-45)= -195

Negative since it’s deeper

this might be yo answer im not sure

i hope this helped u tho

What times what equals -20 and those same numbers added together equals 8

Answers

Answer:

10 and -2

Step-by-step explanation:

I am not understanding this question.

Answers

Answer:

boardgamegeek.com/boardgame/245655/kings-dilemma

Step-by-step explanation:

Which equation represents an inequality in the system of inequalities shown in the graph? Which point is a solution to the system?Which equation represents an inequality in the system of inequalities shown in the graph? Which point is a solution to the system?

Answers

The equation that represents an inequality in the system of inequalities shown in the graph is;

y < 2x + 2

The point that is a solution to the system is; (-1, -2)

Graph Inequalities

The image of the graph is missing and so i have attached it.

From the graph, we see one broken line passing through the points x = -1 and y = 2.

We also see an unbroken line passing through the points x = ½ and y = -1

Now, when we use a broken line it means greaterthan or less than but when we use a thick line which is unbroken it means y ≤ or y ≥.

Now, if we shade below the line, it is (y< or y≤) but if we shade above the line, it is (y> or y≥).

Now, we see that the solution will be in between the broken line and the thick line.

Thus, the equation is;

y < 2x + 2 with the solution as coordinates as (-1, -2)

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Answer:

y<2x+2

(-1,-2)

explanation:

person above gets credit, hope it helps!

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