Please put the explanation!

Mathematics

1 answer:

BaLLatris [955]3 years ago

5 0

Answer:

Step-by-step explanation:

In order to get this answer, we must know that a triangle's angles add up to exactly 180. Also, Angles that intersect will have congruent, opposite sides. The last thing is that a line is = 180 degrees. So, the triangle with the 94 and the 142, you can use that. the angle next to the 142 is going to be 180-142 which is 38 and since the other angle is opposite 94, as well. when you add those up u get 132 and 180-132= 48 which is the missing angle for the far right triangle. then, you get the opposite of that angle, put that in the other triangle, do the same with the 72, and add those up to get 120 and since a triagle adds up to 180, 180-120 = 60. So, 60 is your missing angle. Cheers

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a) $n=\frac{0.675(1-0.675)}{(\frac{0.02}{1.64})^2}=1475.07$

And rounded up we have that n=1476

b) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.64})^2}=1681$

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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

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

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)

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 90% of confidence, our significance level would be given by $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by: