2. Solve for x
1 answer:
You might be interested in
Answer:
They would know a and b.
a. The mean of this distribution, by the Central Limit Theorem, is the sample mean, and thus, the researches would know this after they took the sample.
b. Sample size is 100 > 30, and thus, by the Central Limit Theorem, they would know that the shape of the distribution is approximately normal.
c. To know the standard deviation of the sampling distribution of the sample mean, the researchers would have to know the population's standard deviation, which they can't get for the sample. So they would not know the standard deviation of the sampling distribution of the sample mean after they took the sample.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
a. The value of the mean of the sampling distribution of the sample mean.
The mean of this distribution, by the Central Limit Theorem, is the sample mean, and thus, the researches would know this after they took the sample.
b. The approximate shape of the sampling distribution of the sample mean.
Sample size is 100 > 30, and thus, by the Central Limit Theorem, they would know that the shape of the distribution is approximately normal.
c. The standard deviation of the sampling distribution of the sample mean.
To know the standard deviation of the sampling distribution of the sample mean, the researchers would have to know the population's standard deviation, which they can't get for the sample. So they would not know the standard deviation of the sampling distribution of the sample mean after they took the sample.
Remember that for a quadratic function of the form 
we can find its vertex with formula: 
where 
is the x-coordinate of the vertex; then we will find the y-coordinate by replacing in our original function.
From the question know that
and 
, so lets replace those values in our vertex formula to find the x-coordinate of our vertex:
Now lets replace that value into our original function to find the y-coordinate of our vertex:
Finally, we have our vertex (6,-9)
Now to graph our function we are going to take advantage of its line of symmetry; if the vertex is (6,-9) the line of symmetry of the parabola is x=6, so if we chose the point (6,0), our second point will have coordinates (3,0) as you can see in the picture.
From the question know that
Now lets replace that value into our original function to find the y-coordinate of our vertex:
Finally, we have our vertex (6,-9)
Now to graph our function we are going to take advantage of its line of symmetry; if the vertex is (6,-9) the line of symmetry of the parabola is x=6, so if we chose the point (6,0), our second point will have coordinates (3,0) as you can see in the picture.