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cricket20 [7]
3 years ago
13

What is 258/300 as a percent

Mathematics
2 answers:
Step2247 [10]3 years ago
4 0
To transform it into percent we want to have 100 into denominator. The easiest way is divide numerator and denominator by 3 (thats because than it doesnt change the value of fraction), so:
\frac{258}{300}= \frac{258:3}{300:3}= \frac{86}{100} = 86% - its the result
katrin2010 [14]3 years ago
3 0
258\ \ |\ \ :2\\129\ \ |\ \ :3\\43\ \ \ \ |\ \ :43\\1\\\\258=6\cdot43\\\\300\ \ |\ \ :2\\150\ \ |\ \ :2\\75\ \ \ \ |\ \ :3\\25\ \ \ \ | \ \ : 5\\5\ \ \ \ \ |\ \ :5\\1\\\\300=6\cdot50\\\\ \frac{\big{258}}{\big{300}} =\frac{\big{6\cdot43}}{\big{6\cdot50}} =\frac{\big{43}}{\big{50}}

\\\\\frac{\big{43}}{\big{50}} =\frac{\big{43}}{\big{50}} \cdot 100\%=\frac{\big{43}}{\big{50}} \cdot 50\cdot2\%=43\cdot2\%=86\%
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Answer:

a) n=(\frac{1.960(16)}{5})^2 =39.33 \approx 40

So the answer for this case would be n=40 rounded up to the nearest integer

b) For this case if we see the formula for the margin of error

ME=z_{\alpha/2}\frac{s}{\sqrt{n}}    (a)

We can see that the margin of error is inversely proportional to the sample size so if we want a samller margin of error we need a LARGER sample

Answer: LARGER

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".

\bar X represent the sample mean for the sample  

\mu population mean

\sigma=16 represent the population standard deviation

n represent the sample size  

Solution to the problem

Part a

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{s}{\sqrt{n}}    (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got z_{\alpha/2}=1.960, replacing into formula (b) we got:

n=(\frac{1.960(16)}{5})^2 =39.33 \approx 40

So the answer for this case would be n=40 rounded up to the nearest integer

Part b

For this case if we see the formula for the margin of error

ME=z_{\alpha/2}\frac{s}{\sqrt{n}}    (a)

We can see that the margin of error is inversely proportional to the sample size so if we want a samller margin of error we need a LARGER sample

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