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STALIN [3.7K]
3 years ago
8

I am stuck and I hate maths so please help me

Mathematics
1 answer:
Scilla [17]3 years ago
3 0

Answer:

h = 21.2 cm

Step-by-step explanation:

You know the measure of one acute angle. It is 23 deg.

For that acute angle, the 9-cm leg is the opposite leg, and the h-cm leg is the adjacent leg. The trig ratio that relates the opposite leg to the adjacent leg is the tangent.

\tan A = \dfrac{opp}{adj}

\tan 23^\circ = \dfrac{9}{h}

h \tan 23^\circ = 9

h = \dfrac{9}{\tan 23^\circ}

h = \dfrac{9}{0.4245}

h = 21.2

Answer: h = 21.2 cm

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Answer:

n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

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".  

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Solution to the problem

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)  

If solve n from equation (a) we got:  

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

The margin of error desired for this case is ME= \pm 0.02 equivalent to 2% points

For this case we need to assume a confidence level, let's assume 95%. And since we don't have prior estimation for the population proportion of interest the best value to do an approximation is \hat p =0.5

In order to find the critical value we need to take in count that we are finding the margin of error 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}=\pm 1.96  

Now we have all the values needed and if we replace into equation (b) we got:

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So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

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