What are 3 features of a normal distribution?
1. Bell-shaped
2. Symmetrical
3. The mode, median, and mean are equal
When is a distribution treated as a normal distribution?
If it's roughly symmetrical
What is 1 con about the normal distribution?
Most distributions are theoretical, as a true normal distribution is rare to find in nature
What is a Z score (or, standard deviation value)?
The number of standard deviations a given raw score falls above or below the mean
What are Z scores 'converting'?
Raw data (cases/single observations) into standard deviation units, where 1 'S.D unit' constitutes 1 step away from the mean of a distribution
What is the mean when it's expressed as a Z score?
Always 0, since it's 0 'steps' away from itself
What is the standard normal distribution?
A normal distribution represented as Z scores where mean = 0 and standard deviation = 1
Approximately what % of a standard normal distribution is within 2 S.D units of the mean? (1 above and 1 below?)
68%
Approximately what % of a standard normal distribution is within 4 S.D units of the mean? (2 above and 2 below?)
95%
Approximately what % of a standard normal distribution is within 6 S.D units of the mean? (3 above and 3 below?)
99.7%
What is the "68%-95%-99.7% Rule"?
A normally distributed data set has a constant relationship with it's standard deviation. such that, a given S.D above/below the mean will always account for the same proportion (%) of data under the curve
What is a Z table (standard normal table)?
A table that, if given a Z score, can determine the probability (% or chance) of a given raw score falling under a specific area of a curve, or, for calculating the area under a curve between any two points
If the scores of an IQ test are normally distributed with a mean of 100 and a standard deviation of 10, what % of students will score above 105?
- What are the steps to solve this?
30.8%
1. Use the raw score to find the Z score using the correct formula
2. Find the corresponding value on the z-table
3. SUBTRACT that value from 1.00 since Z scores always represent less than (<)/to the left and we're interested in greater than (>)/to the right
If the scores of an IQ test are normally distributed with a mean of 100 and a standard deviation of 10, what % will score between 97 and 103?
- What are the steps to solve this?
23.5%
1. use BOTH raw scores to find their Z scores using the correct formula
2. Find their corresponding values on the z-table
3. subtract from EACH OTHER to find the area under the curve between the two scores
If the scores of an IQ test are normally distributed with a mean of 100 and a standard deviation of 10, how high would one need to score to be in the 95th percentile?
- What are the steps to solve this?
116.5
1. Find the corresponding value on the z-table that best matches the 95th percentile (95%)
2. Find it's corresponding Z score
3. Use the raw score formula to convert the Z score back into a raw score
Z scores use probability of what % of the area under the curve falls below or to the left of a given Z score, how do you find out % of the area under the curve falls to the right of a Z score?
Subtract the Z score from 1.00 since the distribution has to be 100% = 1.00. If a Z score represents what's to the left, and you subtract it from 1.00, anything left over must be what's to the right of the Z score