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Korolek [52]
2 years ago
10

Triangle angle sum theorem What is the value of z?

Mathematics
2 answers:
s344n2d4d5 [400]2 years ago
8 0

→32+76+24z=180

[Sum of all sides of a triangle]

→108+24z=180

→24z=180-108

→z= \frac{72}{24}

→z = 3

prisoha [69]2 years ago
7 0

Answer:

z=3

Step-by-step explanation:

→32+76+24z=180[Sum of all sides of a triangle]

→108+24z=180

→24z=180-108

→z=72/24

→z=3

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Answer:

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So on this case the 90% confidence interval would be given by (45.39;62.61)    

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=54 represent the sample mean  

\mu population mean (variable of interest)

\sigma=21 represent the sample standard deviation

n=16 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 0.90 or 90%, the value of \alpha=1-0.9=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=1.64

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

54-1.64\frac{21}{\sqrt{16}}=45.39    

54 +1.64\frac{21}{\sqrt{16}}=62.61    

So on this case the 90% confidence interval would be given by (45.39;62.61)    

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3 years ago
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