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nikitadnepr [17]
3 years ago
8

How to Find x value: 9-0.75(x+8)-5=-6.5

Mathematics
1 answer:
Dahasolnce [82]3 years ago
8 0
Here's how to find the value of x:

<span>9 - 0.75 ( x + 8 ) - 5 = -6.5      find the difference of 9 - 0.75

</span><span>8.25 ( x + 8 ) - 5 = -6.5           add 5 to both sides
</span>
8.25 ( x + 8 ) = -1.5                distribute 8.25 to x and 8

8.25x + 66 = -1.5                    subtract 66 from both sides

8.25x = -67.5                          divide both sides by 8.25

x = 18.18181818......            the value of x is 18 2/11

hope this helps
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652.6-2.01\frac{311.7}{\sqrt{50}}=563.997    

652.6+2.01\frac{311.7}{\sqrt{50}}=741.203    

So on this case the 95% confidence interval would be given by (563.997;741.203)    

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=652.6 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=311.7 represent the sample standard deviation

n=50 represent the sample size  

Soltuion to the problem

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=50-1=49

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that t_{\alpha/2}=2.01

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

652.6-2.01\frac{311.7}{\sqrt{50}}=563.997    

652.6+2.01\frac{311.7}{\sqrt{50}}=741.203    

So on this case the 95% confidence interval would be given by (563.997;741.203)    

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