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Lunna [17]
3 years ago
7

Increase 3000 by 5.4%

Mathematics
1 answer:
katen-ka-za [31]3 years ago
6 0
------------------------------------
Original Number
------------------------------------
3000

------------------------------------
Increase
------------------------------------
5.4% of 3000
= 0.054 x 3000
= 162

------------------------------------
New Total
------------------------------------
3000 + 162 = 3162

------------------------------------
Answer: 3162
------------------------------------
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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".  

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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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ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

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

Since we don't have a prior estimation for th proportion of interest, we can use this value as an estimation \hat p =0.5 And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.04}{2.58})^2}=1040.06  

And rounded up we have that n=1041  or higher.

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