Answer:
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Step-by-step explanation:
The Central Limit Theorem estabilishes 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 proportions, the mean is
and the standard deviation is 
In this problem, we have that:
.
So


The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Answer: The required value of f(3) is 81.
Step-by-step explanation: We are given the following function :

We are to find the value of f(3).
Substituting x = 3 in equation (i), we get

Thus, the required value of f(3) is 81.
Answer:
Dilation changes (x,y) values not the grid or coordinate plane. Basically, dilating a graph or a coordinate grid means the original coordinates you may have had will be changed with the dilation. For example, a triangle plotted had its original area of 26 dilated to an area of 58.
Answer:
Step-by-step explanation:
Given that
Slope m=-3
A point (x, y)=(4,-2)
Equation of a line can generally be written as
y=mx+c
Where, m is the slope
And c is the intercept on y-axis
Since we are given m=-3
Then, y=mx+c becomes
y=-3x+c
To get c, let substitute the point given, i.e x=4 and y=-2
y=-3x+c
-2=-3(4)+c
-2=-12+c
-2+12=c
c=-2+12
c=10
y=mx+c, then m=-3 and c=10
Then, the equation the line becomes y = -3x + 10
This is the required line equation
Answer:
120 x 10^3
7 x 10^5
9 x 10^4
Step-by-step explanation: