Characteristics
What is the shape of the graph of a normal distribution?
Bell-shaped
A normal distribution has a mean of 8 and a standard deviation of 2. What value is 2 positive standard deviations away from the mean?
12
What is the mean of a standard normal distribution?
Zero
What is the formula for converting raw scores to z-scores?
"(data value – mean) ÷ (standard deviation)"
For a normal distribution, find the z-score that separates the highest 30% from the rest of the distribution.
z=0.52
What measure of central tendency of a normal distribution represents the highest point on the curve?
Mean
A normal distribution has a mean of 15 and a standard deviation of 3. What value is 3 negative standard deviations away from the mean?
6
What is the standard deviation of a standard normal distribution?
One
A normal distribution has a mean of 7 and a standard deviation of 2.5. What z–score corresponds to a raw score of 10 for this distribution?
1.2
For a normal distribution, find the z-score that separates the lowest 40% from the rest of the distribution.
z=-0.25
What percentages roughly represent the percent of the data values that fall within one, two, and three standard deviations from the mean of a normal distribution?
68–95–99.7%
A normal distribution has a mean of 10 and a standard deviation of 1. What percentage of data values that fall between the values of 8 and 12?
95.4%
In a standard normal distribution, we use z-scores to find percentages of the data that fall within a certain range. What standard deviation from the mean represents one z-score?
One
A normal distribution has a mean of 84 and a standard deviation of 4. What percentage of the data of this distribution that falls below 78?
6.68%
For a normal distribution, find the z-score that separates the highest 75% from the rest of the distribution.
The normal curve is _________ with respect to its mean.
Symmetric
A normal distribution has a mean of 24 and a standard deviation of 6. 68.3% of the values of this distribution fall between what two data values?
18 and 30
It refers to a data value that is an element of a non-standard distribution.
Raw Score
What percentage of the data of a distribution that lies between a z–score of 0 and –1.38?
41.62%
Scores on the SAT form a normal distribution with a mean of 500 and standard deviation of 100, Find the range of z-values that defines the middle 80% of the distribution of SAT scores.
-1.28<z<1.28
What is the total area under the curve of a normal distribution?
One
A normal distribution has a mean of 100 and a standard deviation of 10. What percentage of data values will fall between the values of 70 and 90?
15.7
Why do we use the standard normal curve by converting raw scores to z-scores?
"So that we can easily determine what percentage of our data falls within a specific range that is not exactly 1, 2, or 3 standard deviations away from the mean"?
A normal distribution has a mean of 50 and a standard deviation of 6. What percentage of the data of this distribution that falls above 61?
3.36%
The Welcher Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of 35 and a standard deviation of 6.Assuming these raw scores form a normal distribution, what test score represents the 65th percentile?
37.31