Conceptual section
1. Why is the normal distribution important to statistics?
One reason is that there are many variables that have distributions that closely resemble normal distributions, and it provides a good model for the sampling distribution of many statistics.
2. What characteristics do all normal distributions have?
All normal distributions, regardless of mean and variance, have their points of inflection one standard deviation below and above the mean. More importantly, regardless of the specific mean and variance, all normal distributions share the same area between standard deviations.
3. What percentage of the normal distribution falls above the mean?
For normal distributions, there is approximately 34% of the area between the mean and one standard deviation away from the mean.
Approximately what percentage of the normal distribution falls between the mean and one standard deviation above it?
Between one and two standard deviations from the mean, on either side, is approximately 14% of the area.
Approximately what percentage falls in the area between one and two standard deviations above the mean?
More than two standard deviations from the mean are the final 2%.
4. What value does the mean of the unit-normal distribution always equal?
It is always equal to zero. What value does its standard deviation always equal?
Is always equal to 1. 0 How can we use the unit-normal distribution to compare other normal distributions?
The unit distribution is a normal distribution composed of z-scores. You can do this by using it to equate the area and probability.
5. How would we find the area under the curve above a particular raw score?
You find the area by converting the raw to a z-score; you then have to subtract the area.
6. How would we find the area under the curve between two raw scores?
You find the area of the mean for the z-score after you convert the raw scores then you do so by subtracting the lower value z-score.
7. When does the binomial distribution begin to resemble a normal distribution?
When we convert it to a z-score.
8. What is the sampling distribution of the mean?
The sampling distribution is the probability distribution for a random variable. The sampling distribution of the mean is the distribution of the averages of the raw scores.
What happens to its shape as the size of its samples gets larger?
As n increases, the binomial distribution starts to resemble a normal distribution that gets narrower and has less error.
How does the grand mean compare to the mean of the raw score distribution?
Sample means will become normal even if the raw scores are not. Skewness and Kurtosis for the sam...
