The point A(–1, 4) is translated five units right and three units down. Which rule describes the translation?
2 answers:
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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:
The train can be made up in a total of ways
Step-by-step explanation:
FIrst, lets assume that all cars are distinct. If that is the case, then, since we have a total of 8 cars, we have
- 8 possibilities for the first car
- 7 possibilities for the second car
- 6 possibilities for the third car
and so on.
So we have a total of 8! = 8*7*6*...*3*2*1 possibilities to make a train.
Now lets take into account that 5 of the cars are identical within each other. Then we could make a permutation of those 5 cars and we wouldnt notice. Hence, the order of the 5 cars of second-class doesnt matter and as a result, we should divide 8! by the total of possible permutations of the 5 second class cars, that it, 5!
We also need to divide the result by 2! = 2, because which first class car came first doesnt matter either. Therefore, the train can be made up in a total of ways.