Question

1.

The empirical rule says that 95% of the population is within 2 standard deviations of the mean, but when I find the z-scores that mark off the middle 95% of the standard normal distribution I calculate -1.96 and 1.96. Is this a contradiction? Why or why not? In other words why are the normal distribution calculators not agreeing with the empirical rule? [2 sentences]

2.

Answer the following:

What is a sampling distribution?

[2 sentences]

What is the Central Limit Theorem?

[2 sentences]

What is the effect of increasing sample size on a sampling distribution? [1 sentence]

Why is the standard deviation of the sampling distribution smaller than the standard deviation of the population from which it came?

[1 sentence]

Answer 1

Answer:

1.

As should be obvious, - 2 and 2 are near - 1.96 and 1.96.

The observational standard is only an estimation (for down to earth purposes), so that clarifies the fine contrast.

Anyway, they concur (they don't repudiate), we simply have a round off blunder here (for down to earth purposes).

2.

The central limit theorem states that in the event that you have a populace with mean μ and standard deviation σ and take adequately huge arbitrary examples from the populace with replacement, at that point the appropriation of the example means will be around regularly circulated. This will remain constant paying little mind to whether the source populace is typical or slanted, gave the example size is adequately enormous (more often than not n > 30). In the event that the populace is ordinary, at that point the hypothesis remains constant in any event, for tests littler than 30)

What is the effect of increasing sample size on a sampling distribution?

Here as the sample size i.e., n increases then the standard error of mean i.e. decreases and sampling distribution of sample means is more closely follows the normal distribution.

Why is the standard deviation of the sampling distribution smaller than the standard deviation of the population from which it came ?

Here it is given as follows

i.e.,

=

As standard deviation of sampling distribution will be smaller than population standard deviation.