Using the <em>normal distribution and the central limit theorem</em>, it is found that the power of the test is of 0.9992 = 99.92%.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation .
In this problem:
- The mean is .
- The standard deviation is .
- A sample of 30 is taken, hence .
The power of the test is given by the probability of a sample mean above 8, which is <u>1 subtracted by the p-value of Z when X = 8</u>, so:
By the Central Limit Theorem:
has a p-value of 0.0008.
1 - 0.0008 = 0.9992.
The power of the test is of 0.9992 = 99.92%.
To learn more about the <em>normal distribution and the central limit theorem</em>, you can check brainly.com/question/24663213
Answer:
k=−0.8
Step-by-step explanation:
Start with the equation: 0.2(3k+1)=-0.4-(-0.2-0.1K)
Use distributive property on each side of the equation. For the left side, distribute 0.2 into 3k and 1, and for the right side, distribute -1 into -0.2 and -0.1k. (We use a -1 because the negative sign on the outside of the parenthesis is equivalent to -1)
(0.2)(3k) + (0.2)(1) = 0.6k + 0.2
(-1)(-0.2) + (-1)(-0.1k) = 0.2 + 0.1k
New equation: 0.6k + 0.2 = -0.4 + 0.2 + 0.1k
Now we can combine like terms on the right side. (-0.4 and 0.2)
0.6k + 0.2 = 0.1k - 0.2
Now to get rid of k on one side, we can subtract 0.1k from the right side.
(0.6k - 0.1k) + 0.2 = (0.1k - 0.1k) - 0.2
0.5k + 0.2 = -0.2
Now we need to get 0.5k by itself, so we'll subtract the 0.2 on both sides.
0.5k + (0.2 - 0.2) = (-0.2 - 0.2)
0.5k = -0.4
To get k by itself, we must divide both sides by 0.5.
(0.5k / 0.5) = (-0.4 / 0.5)
k = -0.8
Answer:
X=3/2 or 1.732
Step-by-step explanation:
X^2-4+1=0
Combine like terms
-4 + 1 = -3
X^2-3=0
add 3 to both sides
X^2= 3
X= 3/2
Reduce the expression<span> by cancelling the </span><span>common factors</span><span>.
</span><span>9/20
</span>Exact Form:
<span>9/20</span>
<span>Decimal Form: </span>
0.45
Answer:
Han's mixture, Claire's mixture
Step-by-step explanation:
I figured out the percentage of orange juice for each person's mixture:
For Claire:
2 1/2 + 1/3 = 2 5/6
2 5/6 as a decimal: about 2.8
Now find what percent of Claire's total mixture was orange juice:
100 * 1/3 / 2.8 = about 11.9%
For Han:
1 2/3 + 1/4 = 1 11/12
1 11/12 as a decimal: about 1.9
Now find what percent of Han's total mixture was orange juice:
100 * 1/4 / 1.9 = 13.2%
So, Han's mixture is stronger, since his has the higher percentage of orange juice concentrate