Mathematics, 24.03.2020 05:37 nmorin603p3rhkg

We would like to estimate the proportion of UF students who owns a scooter to within 1% of the truth, with 95% confidence. We believe around 10% of students do. How many students should be sampled?

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Answer from: alissa2151

The estimated proportion for this case is $\hat p = 0.1$

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

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

$n=\frac{0.1(1-0.1)}{(\frac{0.01}{1.96})^2}=3457.44$

And rounded up we have that n=3458

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)

The estimated proportion for this case is $\hat p = 0.1$

And on this case we have that $ME =\pm 0.01$ 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)

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

$n=\frac{0.1(1-0.1)}{(\frac{0.01}{1.96})^2}=3457.44$

And rounded up we have that n=3458

Answer from: Quest

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length

Brainliest and 75 points for whoever can explain how to get these given: △acm, m∠c=90°, cp⊥ am. ap=

Answer from: Quest

The question is kind of confusing. if it's asking how many variations of answers can you give. then do 4^5 for your answer.this would be something like the first question could be a and the 2nd c or first b next c etc. if you can, ask the teacher for a better confirmation of what it's asking. if i'm assuming correctly what it's asking, it's 625 different variations.