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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The correct answer would be A.
We can immediately eliminate C and D because they have the slope listed as 2 rather than -2.
Because we're looking for the line that passes through (1, 5), we know that the y-intercept has to be 7, because from (0, 7) we get to (1, 5) when we apply the slope of -2.
Thus, the answer is A.
Answer:
<h2>
WX = 3√2 units </h2>
Step-by-step explanation:
Using the formula for calculating the distance between two points to calculate the length of WX.
D = √(y₂-y₁)²+(x₂-x₁)²
Given the endpoints W(2,-7) and X(5,-4), x₁ = 2, y₁ = -7, x₂ = 5 and y₂ = -4
Substituting this values into the formula to get the length of WX will give;
WX = √(-4-(-7))²+(5-2)²
WX = √(-4+7)²+3²
WX = √3²+3²
WX = √18
WX = √2*9
WX = 3√2 units
Hence the length of WX is 3√2 units.
Answer:
h<-8/3
Step-by-step explanation:
collect like terms
-10h+7h>9-1
3h>8
divide both sides of the inequality by -3 and flip the inequality sign
h<-8/3
Answer:
this an example not the answer i don't know the answer
E is between D and F.
Given: E is between D and F
Prove: DE = DF − EF.
Statements Reasons
1. E is between D and F Given
2. D, E, and F are collinear points, and E is on ¯DF Definition of between
3. DE + EF = DF Segment Addition Postulate
4. DE = DF − EF Subtraction property of equality
2. If →BD divides ∠ABC into two angles, ∠ABD and ∠DBC, then m∠ABC = m∠ABC - m∠DBC.
Step-by-step explanation:
