Which of the following statements about the sampling distribution of the sample mean, x-bar, is not true? A. The sampling distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough. B. The sampling distribution is normal regardless of the sample size, as long as the population distribution is normal. C. The sampling distribution's mean is the same as the population mean. D. The sampling distribution's standard deviation is smaller than the population standard deviation. E. All of the above statements are tru

E. All of the above statements are true

Step-by-step explanation:

The mean of sampling distribution of the mean is simply the population mean from which scores were being sampled. This implies that when population has a mean μ, it follows that mean of sampling distribution of mean will also be μ.

It should also be noted that the distribution's shape is symmetric and normal and there are no outliers from its overall pattern.

The statements about the sampling distribution of the sample mean, x-bar that are true include:

• The sampling distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough.

• The sampling distribution is normal regardless of the sample size, as long as the population distribution is normal. • The sampling distribution's mean is the same as the population mean.

• The sampling distribution's standard deviation is smaller than the population standard deviation.

Therefore, option E is the correct answer as all the options are true.

The option that gives the true statement about sampling distribution of the sample mean, x-bar, is;

Option E: All of the above.

Let us access each of the options;

A) There is a condition for normal distribution which states that sample size must be more than 30. So as long as the sample size is big enough, regardless of the shape, it is still a normal distribution.

B) This statement is also true because as long as the distribution of the population is normal, then it overrules every other thing as the sample distribution will have to be normal as a result.

C) This is true because by definition of population mean, it is the same as sample mean of the distribution.

D) This is true because the population is always more than the sample.

E) This is correct as all the above options are true.

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step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be