Normal Distribution and Central Limit Theorem

Flashcards based on lecture notes about normal distribution and the central limit theorem.

Normal distribution is ___.

A distribution defined by its mean (mu) and standard deviation (sigma), which is the inflection point on the bell curve.

A random variable is __.

Something you don't know what value it's going to take on in advance.

According to the law of large numbers for bootstrap distributions ___.

The mean of all the means that you compute from all those bootstrap samples will be the same as the original mean of the sample.

In the bootstrap distribution of commute times, we look at the area under the right-hand tail above 31 when interested in ___.

The proportion of bootstrap mean commute times over 31.

The normal density function has a problem:__.

It does not have an antiderivative.

To compute areas under different normal distributions, rather than finding individual distributions, __.

We would convert these values into a z value.

A z value is .

Is just the number of standard deviations from the mean.

Within one standard deviation either side of the mean for any normal distribution will always include __.

68% of the values.

What is critical when comparing values from different normal distribution is __.

The number of standard deviations you are from the mean within your distribution.

The standard normal distribution is __.

A normal distribution which has a mean of zero and a standard deviation of one.

Once you translate the x's into z's, __.

We say that distributions have been standardized.

To calculate what score in the SAT would be two standard deviations above the mean, __.

You take your five eighty plus two times 70.

The central limit theorem is __.

The single most important result in ECMT1010 that ties everything together, allowing normal approximations for bootstraps and randomizations.

If the sample size is large enough, the sampling distribution of a mean __.

Is normally distributed and centered on mu.

When you select repeated samples randomly from a population regardless of its underlying distribution, __.

That distribution will have a normal density.

For the central limit theorem, a sample size is large enough __.

As long as the sample size is 30.

The central limit theorem will still work if the sample size is less than 30, but, __.

You require that the original population is normally distributed.

For categorical variables to use the central limit theorem__.

You need a sample size that gives you a count of at least 10 in each category.

When the instructions mention using both methods, it means ___.

Statistical methods that were mentioned on the previous slide, the bootstrap and the normal approximation.

Under standardization of normal distributions__.

For a 90% confidence interval, that is 1.645 standard deviations either side of the mean in the standardized normal distribution.