Using the t-distribution to build the 99% confidence interval, it is found that:
- The margin of error is of 3.64.
- The 99% confidence interval for the population mean is (19.36, 26.64).
<h3>What is a t-distribution confidence interval?</h3>
The confidence interval is:
![\overline{x} \pm t\frac{s}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%5Cpm%20t%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D)
In which:
is the sample mean.
- s is the standard deviation for the sample.
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 21 - 1 = 20 df, is t = 2.086.
The other parameters are given as follows:
![\overline{x} = 23, s = 8, n = 21](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%3D%2023%2C%20s%20%3D%208%2C%20n%20%3D%2021)
The margin of error is given by:
![M = t\frac{s}{\sqrt{n}} = 2.086\frac{8}{\sqrt{21}} = 3.64](https://tex.z-dn.net/?f=M%20%3D%20t%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%202.086%5Cfrac%7B8%7D%7B%5Csqrt%7B21%7D%7D%20%3D%203.64)
Hence the bounds of the interval are:
![\overline{x} - M = 23 - 3.64 = 19.36](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20-%20M%20%3D%2023%20-%203.64%20%3D%2019.36)
![\overline{x} + M = 23 + 3.64 = 26.64](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%2B%20M%20%3D%2023%20%2B%203.64%20%3D%2026.64)
The 99% confidence interval for the population mean is (19.36, 26.64).
More can be learned about the t-distribution at brainly.com/question/16162795
#SPJ1
Answer:
2
5
![\dfrac{4}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B5%7D)
Step-by-step explanation:
We are given 2 fractional numbers:
![1.\ \dfrac{2}4\\2.\ \dfrac{5}8](https://tex.z-dn.net/?f=1.%5C%20%5Cdfrac%7B2%7D4%5C%5C2.%5C%20%5Cdfrac%7B5%7D8)
We have to use fraction strips to compare to the fractional numbers.
Let we are Comparing
with the length of
number of
sections.
i.e.
![\dfrac{2}{4} = x \times \dfrac{1}{4}\\\Rightarrow x = \dfrac{2 \times 4}{4}\\\Rightarrow x = 2](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B4%7D%20%20%3D%20x%20%5Ctimes%20%5Cdfrac%7B1%7D%7B4%7D%5C%5C%5CRightarrow%20x%20%3D%20%5Cdfrac%7B2%20%5Ctimes%204%7D%7B4%7D%5C%5C%5CRightarrow%20x%20%3D%202)
Let we are Comparing
with the length of
number of
sections.
i.e.
![\dfrac{5}{8} = y \times \dfrac{1}{8}\\\Rightarrow y = \dfrac{5 \times 8}{8}\\\Rightarrow y = 5](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B8%7D%20%20%3D%20y%20%5Ctimes%20%5Cdfrac%7B1%7D%7B8%7D%5C%5C%5CRightarrow%20y%20%3D%20%5Cdfrac%7B5%20%5Ctimes%208%7D%7B8%7D%5C%5C%5CRightarrow%20y%20%3D%205)
Now, let us have a look at 3rd part of question:
The sections of 2/4 is _____ the length of 5/8. Therefore, 2/4 < 5/8
Let the answer be
.
So, the equation becomes:
![\dfrac{2}{4} = z \times \dfrac{5}{8}\\\Rightarrow z = \dfrac{2 \times 8}{4 \times 5}\\\Rightarrow z = \dfrac{2 \times 2}{5}\\\Rightarrow z = \dfrac{4}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B4%7D%20%3D%20z%20%5Ctimes%20%5Cdfrac%7B5%7D%7B8%7D%5C%5C%5CRightarrow%20z%20%3D%20%5Cdfrac%7B2%20%5Ctimes%208%7D%7B4%20%5Ctimes%205%7D%5C%5C%5CRightarrow%20z%20%3D%20%5Cdfrac%7B2%20%5Ctimes%202%7D%7B5%7D%5C%5C%5CRightarrow%20z%20%3D%20%5Cdfrac%7B4%7D%7B5%7D)
So, the answers are:
2
5
![\dfrac{4}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B5%7D)
Answer:
x= (-2, 0) y=(0, -5)
Step-by-step explanation:
or you could say -2 and -5
Okay and what do you need to find??
I don't see a table but I can give you the means to answer it yourself. The inverse function is represented by this:
![y= \frac{k}{x}](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7Bk%7D%7Bx%7D%20)
where k is your constant. You are given a k value of 4. If you solve this for k then you will get xy=4. In your tables, multiply your x value by your y value within your coordinate points and if you get a product of 4 each time you multiply x by y, then that table is your answer.