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Stels [109]
3 years ago
7

What will the range values be for the function f(g) = 3g - 5 for the domain {-1.5, 2, 4}?

Mathematics
1 answer:
DochEvi [55]3 years ago
5 0
3(-1.5)-5=
-4.5-5=
-9.5

3(2)-5=
6-5=
1

3(4)-5=
12-5=
7

{f(-1.5),f(2),f(4)} = {-9.5,1,7} 
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Answer:

a) n =1623

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Step-by-step explanation:

1) Notation and definitions

n random sample taken

\hat p=0.19 estimated proportion of customers are not satisfied with the service provided by the local dealer

Confidence =0.96 or 96%

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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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The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Part a

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 96% of confidence, our significance level would be given by \alpha=1-0.96=0.04 and \alpha/2 =0.02. And the critical value would be given by:

z_{\alpha/2}=-2.0538, z_{1-\alpha/2}=2.0538

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 0.02 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)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.19(1-0.19)}{(\frac{0.02}{2.0538})^2}=1622.912  

And rounded up we have that n=1623

Part b

The margin of error is given by:

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

So then if w replace the value of n obtained from part a we got:

ME=2.0538\sqrt{\frac{0.21 (1-0.21)}{1623}}=0.0208    

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