Suppose a random sample of 80 measurements is selected from a population with a mean of 25 and a variance of 200. Select the pair that is the mean and standard error of x. a) [25, 2.081]
b) [25, 1.981
c) [25, 1.681]
d) [25, 1.581]
e) [80. 1.681]
f) None of the above

d) [25, 1.581]

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation(which is the square root of the variance) , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation, which is also standard error, .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

So the standard error is:

By the Central Limit Theorem, the mean is the same, so 25.

The correct answer is:

d) [25, 1.581]

answer

see attachment

explanation

the given function is

this function has y-intercept at

-4 and a slope of 2.

note that, the graph has a positive slope.

the graph that represents this function is the straight line that moves upward from left to right.

the graph touches the y-axis at -4.

the correct choice is the graph shown in the attachment.