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Stolb23 [73]
3 years ago
6

Two trains leave stations 272 miles apart at the same time. One train travles 75 miles per hour while the other travles at 95 mi

les per hour. How long will take for the two trains to meet?
Mathematics
1 answer:
VARVARA [1.3K]3 years ago
5 0
102 miles for them to meet up

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Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.13}{2.58})^2}=98.47  

And rounded up we have that n=99

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.  

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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 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:

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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)  

And on this case we have that ME =\pm 0.13 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)  

We assume the value for \hat p =0.5 since we don't have previous info. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.13}{2.58})^2}=98.47  

And rounded up we have that n=99

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