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3 years ago

How do I do number 1 and 2? I've tried them several times, but I still can't get it.

Mathematics

1 answer:

AlladinOne [14]3 years ago

7 0

For question 1, you need to look at the number and decide on the closest square numbers.
For this example, the two closest square numbers to 160 are 144 (12²) and 169 (13²).
Therefore, we can say that the square root of 160 must be between 12 and 13.

For question 2, when we find the area of a 4-sided shape, we have to multiply the 2 adjacent sides. In this case, as the shape is a square when we multiply the 2 sides it is this same as squaring 1 side. This means that when we find the side from an area of a square you take the square root.
We found in question 1 that 13² is 169, therefore the square root is 13 and the sides must each be 13 ft long.

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Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. Whe

kherson [118]

Answer:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.03$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We don't have a prior estimation for the proportion $\hat p$ so we can use 0.5 as an approximation for this case

And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

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3 years ago

How do you do the second part of the problem?

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Answer:

Step-by-step explanation:

According to the Alternating Series Estimation Theorem:

│aₙ₊₁│≤ ε

1 / (4 (n + 1)⁴) ≤ 0.00005

4 (n + 1)⁴ ≥ 20000

(n + 1)⁴ ≥ 5000

n + 1 ≥ 8.41

n ≥ 7.41

n must be an integer, so n ≥ 8.

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3 years ago