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
You would add 4y to both sides of the equation which would leave you with
4y - 3 = 8x
then you would divide the entire equation by 4 leaving you with
y - 3/4 = 2x
then you would add 3/4 to both sides of the equation leaving you with
y = 2x + 3/4
If the town decreases at a rate of 8% per year, it would take 6 years.
100% - 8% = 92%
We would multiply each population per year by 0.92 as the town is decreasing in population by 8% per year
1st year: 18,000 • .92 = 16,560
2nd year: 16,560 • .92 = 15,235.2
3rd year: 15,235.2 • .92 = 14,016.384
4th year: 14,016.384 • .92 = 12,894.72
5th year: 12,894.72 • .92 = 11,863.1424
6th year: 11,863.1424 • .92 = 10,914.091
10,914 is less than 11,000 meaning it would take 6 years for the population to be fewer than 11,000 if the town is decreasing in population at a rate of 8% per year
use the quadrant system to find the area of the polygon shown
44 square units
54 square units
36 square units
52 square units
True 44 square units
C all triangles are different
