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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:
None of the expressions in the option is equal to 10 x(13).
Step-by-step explanation:
The answer can be verified by calculating the values of the expression in the question, those of each options, and then compare as follows:
Value of the expression = 10 x (13) = 10 x 13 = 130
Therefore, we have:
A. 10 + (1+3) = 10 + 4 = 14 130
B. (10 x 1)+3 = 10 + 3 = 13 130
C. 10 + (1x3) = 10 + 3 = 13 130
D. (10 * 1)3 = 10 * 3 = 30 130
Based on the calculations above, none of the expressions in the option is equal to 10 x(13).