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VikaD [51]
3 years ago
13

a window is 12 feet above the ground. a ladder is placed on the ground to reach the window. if the bottom of the ladder is place

d 5 feet away from the building, what is the length of the ladder
Mathematics
1 answer:
marin [14]3 years ago
7 0
A^2+b^2=c^2

12^2+5^2=169

√169= √c^2

13=c so the ladder is 13ft long
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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard devia
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Answer:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (3)

n=(\frac{2.58(54.5)}{5})^2 =790.846 \approx 791

So the answer for this case would be n=791 rounded up to the nearest integer

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 (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

The margin of error is given by this formula:

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

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 (2) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (3)

n=(\frac{2.58(54.5)}{5})^2 =790.846 \approx 791

So the answer for this case would be n=791 rounded up to the nearest integer

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