Can some one help me with reflection

Mathematics

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quester [9]3 years ago

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Step-by-step explanation:

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How large a sample should be selected to provide a 95% confidence interval with a margin of error of 6? Assume that the populati

marshall27 [118]

Using the z-distribution, it is found that a sample of 171 should be selected.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

The margin of error is:

$M = z\frac{\sigma}{\sqrt{n}}$

In which:

$\overline{x}$ is the sample mean.

z is the critical value.

n is the sample size.

$\sigma$ is the standard deviation for the population.

For this problem, the parameters are:

$z = 1.96, \sigma = 40, M = 6$

Hence we solve for n to find the needed sample size.

$M = z\frac{\sigma}{\sqrt{n}}$

$6 = 1.96\frac{40}{\sqrt{n}}$

$6\sqrt{n} = 40 \times 1.96$

$\sqrt{n} = \frac{40 \times 1.96}{6}$

$(\sqrt{n})^2 = \left(\frac{40 \times 1.96}{6}\right)^2$

n = 170.7.

Rounding up, a sample of 171 should be selected.

More can be learned about the z-distribution at brainly.com/question/25890103

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4 0

2 years ago

Nikki packed unit cubes into a prism, as shown. Which statement about the volume of the box is true?

elena-14-01-66 [18.8K]

See the explanation

<h2>Explanation:</h2>

Hello, recall that you need to write complete questions in order to get exact answers. Here we have a missing diagram so I can help you in a general way. A prism is a three dimensional shape that has two identical ends (flat faces

) and the same cross section all along its length. A cube is a special type of prism having six identical square sides. So the volume of a prism given the length of a side as s is:

$V=s^3$