Mathematics: The combined land area of the countries A and B is 159159,973 square kilometers. Country A is larger by 473473 square kilometers. Determine the land area of each country.

The combined land area of the countries A and

Ответ:

ashleyd198308

20.01.2022

Mathematics

The land area of country A and country B are 80223 sq.km. and 79750 sq.km. respectively

Step-by-step explanation:

Let the area of Country B be x

We are given that Country A is larger by 473 square kilometers.

Area of Country A = x+473

Total area of both countries = x+x+473

Total area of both countries = 2x+473

We are given that The combined land area of the countries A and B is 159,973 square kilometers.

So, 2x+473=159973

2x=159973-473

$x=\frac{159973-473}{2}$

x=79750

Area of Country A = x+473=79750+473=80223 sq.km.

Hence the land area of country A and country B are 80223 sq.km. and 79750 sq.km. respectively

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Ответ:

hurricane01

09.10.2021

Mathematics

a) $0.77 - 2.58\sqrt{\frac{0.77(1-0.77)}{40}}=0.5983$

$0.77 + 2.58\sqrt{\frac{0.77(1-0.77)}{40}}=0.9417$

The 99% confidence interval would be given by (0.5983;0.9417) and in a percentage would be:

59.83% < p< 94.17%

b) $0.08 - 1.64\sqrt{\frac{0.08(1-0.08)}{978}}=0.0658$

$0.08 + 1.64\sqrt{\frac{0.08(1-0.08)}{978}}=0.0942$

The 90% confidence interval would be given by (0.0658;0.0942) and in a percentage would be:

6.58% < p< 9.42%

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".

Part a

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 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58$

The confidence interval for the mean is given by the following formula:

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

If we replace the values obtained we got:

$0.77 - 2.58\sqrt{\frac{0.77(1-0.77)}{40}}=0.5983$

$0.77 + 2.58\sqrt{\frac{0.77(1-0.77)}{40}}=0.9417$

The 99% confidence interval would be given by (0.5983;0.9417) and in a percentage would be:

59.83% < p< 94.17%

Part b

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 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The confidence interval for the mean is given by the following formula:

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

If we replace the values obtained we got:

$0.08 - 1.64\sqrt{\frac{0.08(1-0.08)}{978}}=0.0658$

$0.08 + 1.64\sqrt{\frac{0.08(1-0.08)}{978}}=0.0942$

The 90% confidence interval would be given by (0.0658;0.0942) and ina percentage would be:

6.58% < p< 9.42%

0,0(0 оценок)

The combined land area of the countries A and B is 159159,973 square kilometers. Country A is larger by 473473 square kilometers. Determine the land area of each country.

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