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Bumek [7]
3 years ago
15

29.25 + 709-1)

Mathematics
1 answer:
aivan3 [116]3 years ago
8 0

Answer:

I not too sure if this is correct but your answer would be 737.25

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Assume that the helium porosity of coal samples taken from any particular seam is Normally distributed with true standard deviat
riadik2000 [5.3K]

Answer:

a) 4.85-2.33\frac{0.75}{\sqrt{20}}=4.46    

4.85+2.33\frac{0.75}{\sqrt{20}}=5.24    

b) 4.56-2.33\frac{0.75}{\sqrt{16}}=4.12    

4.56+2.33\frac{0.75}{\sqrt{16}}=4.99  

c) n=(\frac{1.960(0.75)}{0.2})^2 =54.02 \approx 55

Step-by-step explanation:

Part a

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

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

The Confidence is 0.98 or 98%, the value of \alpha=0.02 and \alpha/2 =0.01, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that z_{\alpha/2}=2.33

Now we have everything in order to replace into formula (1):

4.85-2.33\frac{0.75}{\sqrt{20}}=4.46    

4.85+2.33\frac{0.75}{\sqrt{20}}=5.24    

Part b

4.56-2.33\frac{0.75}{\sqrt{16}}=4.12    

4.56+2.33\frac{0.75}{\sqrt{16}}=4.99  

Part c  

The margin of error is given by this formula:

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

And on this case we have that ME =0.4/2 =0.2  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(0.75)}{0.2})^2 =54.02 \approx 55

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The photo has the answer

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