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3 years ago

A population has a standard deviation of 5.5. What is the standard error of the sampling distribution if the sample size is 81?

Mathematics

1 answer:

VladimirAG [237]3 years ago

4 0

Answer:

$\sigma = 5.5$

And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution $\bar X$ and for this case we know that the distribution is given by:

$\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error would be:

$\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}$

And replacing we got:

$\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611$

Step-by-step explanation:

For this case we know the population deviation given by:

$\sigma = 5.5$

And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution $\bar X$ and for this case we know that the distribution is given by:

$\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error would be:

$\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}$

And replacing we got:

$\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611$

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Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement

Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.173, n = 120$ . So

$\mu = E(X) = np = 120*0.173 = 20.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14$

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34 - 20.76}{4.14}$

$Z = 3.2$

$Z = 3.2$ has a pvalue of 0.9993

X = 21

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{21 - 20.76}{4.14}$

$Z = 0.06$

$Z = 0.06$ has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

6 0

3 years ago

If you can buy 1/3 of a box of chocolates for 6 dollars how much can you purchase for 4 dollars?

sladkih [1.3K]

$You \: can \: purchase :4 \times \frac{1}{3} \div 6 = \frac{2}{9} \: of \: a \: box$

5 0

4 years ago

Use matrix addition to solve this equation: B + 15 −7 4 0 1 2 = 1 2 12 4 0 2 b11 = b12 = b13 = b21 = 4 b22 = −1 b23 = 0

Arada [10]

Answer:

$b_{11}=-14,b_{12}=9,b_{13}=8,b_{21}=4,b_{22}=-1,b_{23}=0$

Step-by-step explanation:

The given matrix addition is

$B+\begin{bmatrix}15&-7&4\\ 0&1&2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}$

We need to find the elements of matrix B.

Let $B=\begin{bmatrix}b_{11}&b_{12}&b_{13}\\ b_{21}&b_{22}&b_{23}\end{bmatrix}$

Substitute the value of matrix.

$\begin{bmatrix}b_{11}&b_{12}&b_{13}\\ b_{21}&b_{22}&b_{23}\end{bmatrix}+\begin{bmatrix}15&-7&4\\ 0&1&2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}$

After addition of two matrix we get

$\begin{bmatrix}b_{11}+15&b_{12}-7&b_{13}+4\\ b_{21}+0&b_{22}+1&b_{23}+2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}$

On equating both sides.

$b_{11}+15=1\Rightarrow b_{11}=-14$

$b_{12}-7=2\Rightarrow b_{12}=9$

$b_{13}+4=12\Rightarrow b_{13}=8$

$b_{21}+0=4\Rightarrow b_{21}=4$

$b_{22}+1=0\Rightarrow b_{22}=-1$

$b_{23}+2=2\Rightarrow b_{23}=0$

Therefore, the elements of matrix B are $b_{11}=-14,b_{12}=9,b_{13}=8,b_{21}=4,b_{22}=-1,b_{23}=0$ .

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3 years ago

What does this symbol means *

m_a_m_a [10]

Answer:

it's a star

Step-by-step explanation:

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3 years ago

Read 2 more answers

The radius of a circle is 18 meters. What is the circle's area?

ankoles [38]

Answer:

200.96 sq. meters.

Step-by-step explanation:

The formula for the area of a circle is \pi r^(2). To solve for the area, use the given values, pi is 3.14 and the radius is 18. This gives you the new equation of (3.14)(18)^2. Solve algebraically, first raising the radius to the power of 2, and then multiplying.

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3 years ago