The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
<h3>
How to find the confidence interval for population mean from large samples (sample size > 30)?</h3>
Suppose that we have:
- Sample size n > 30
- Sample mean =

- Sample standard deviation = s
- Population standard deviation =

- Level of significance =

Then the confidence interval is obtained as
- Case 1: Population standard deviation is known

- Case 2: Population standard deviation is unknown.

For this case, we're given that:
- Sample size n = 90 > 30
- Sample mean =
= 138 - Sample standard deviation = s = 34
- Level of significance =
= 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).
At this level of significance, the critical value of Z is:
= ±1.645
Thus, we get:
![CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90]](https://tex.z-dn.net/?f=CI%20%3D%20%5Coverline%7Bx%7D%20%5Cpm%20Z_%7B%5Calpha%20%2F2%7D%5Cdfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%5C%5CCI%20%3D%20138%20%5Cpm%201.645%5Ctimes%20%5Cdfrac%7B34%7D%7B%5Csqrt%7B90%7D%7D%5C%5C%5C%5CCI%20%5Capprox%20138%20%5Cpm%205.896%5C%5CCI%20%5Capprox%20%5B138%20-%205.896%2C%20138%20%2B%205.896%5D%5C%5CCI%20%5Capprox%20%5B132.104%2C%20143.896%5D%20%5Capprox%20%5B130.10%2C%20143.90%5D)
Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
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1/4 saved, 3/4
1/3 of the rest (4/4-1/4=3/4, 3/4=rest)
1/3 of 3/4=3/12=1/4
saved=1/4
spent on t-shirt=1/4
CD=?
1/4+1/4+?=4/4
2/4+?=4/4
minus 2/4
?=2/4
?=1/2
spent 1/2 on CDs
Answer: I believe it would be the hypotenuse, i not to sure but I hope this helps in some way
Step-by-step explanation:
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Answer:
The new points would be (-7, -1), (-3, -2) and (-8, 1). The angle would not change
Step-by-step explanation:
When you rotate points by 180 degrees, you simply change the sign on the ordered pairs. This will give you the new points.
Also, spinning the points will not change the angle between them. Therefore it stays the same.