What type of limacon is graphed by the polar equation r=4+2sinttheta?
2 answers:
Answer:
The graph is a convex limacon.
Step-by-step explanation:
Polar equation is defined as
and
Types of limacon:
1. If b < a, then graph is a limacon with and inner loop.
2. If a < b < 2a, then graph is a dimpled limacon.
3. If 2a ≤ b, then graph is a convex limacon.
The given equation is
Here b=4 and a=2.
Since 2a ≤ b, therefore the graph is a convex limacon.
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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