Chapter 6: Part 1 Flashcards
What do normal probability distributions allow us to make?
Inferences about all kinds of data
What have mathematicians determined about normal distributions?
That they follow regular patterns, and by knowing the characteristics we can make inferences about data
What can we use the standard normal table to determine?
The z-score that marks off a certain proportion of a population
What can the normal distribution be used in place of?
The binomial distribution to determine probabilities when there are large numbers of observations
What does a values position on the chart indicate?
Where a data point is relative to the others, both in terms of the value itself, but also in terms of frequency
What will the distribution chart for any variable have?
Values and units of the variable on the x-axis and the frequency on the y-axis
What does a normal distribution tell us for any particular value of the variable?
How common the value is, how far it is from the mean (above or below)
What does the mean define?
Where the center of each distribution will be
What does the standard deviation define?
The spread of the distribution
What do narrower distributions have?
Smaller standard deviations
What do wider distributions have?
Larger standard deviations with more variability among the values
What is the formula for standard deviation?
o = square root o^2 (square root of the variance)
What are the three properties of a normal curve?
Symmetric about the mean, all three measures of central tendency are the same, proportion of areas between the standard deviations are known
What do the three properties of a normal curve create?
Family resemblance among the distributions of all variables that are normally distributed
In a normal curve what are the sections of the normal curve defined by the standard deviation?
The same regardless of the value of the standard deviation
What is a z-score?
Converts any individual raw value into a score that tells us how far that score is from the mean in terms of the standard deviation
What is the standard normal distribution?
Makes it easier to apply the properties of the normal distribution to data collected on different scales
What does combining z-scores with properties of the normal distribution allow us to know?
Where a score is relative to mean but also how much of the distribution falls above and below it
What does the standard normal table tell us about z-scores?
What values are to the left of the z-score
What do you do to find the value above a certain percentage from the z-score table?
You take the value that is below and subtract it from 1 to get the score of the value above
How do you find the area between a z-score and the mean?
You can subtract the area given in the standard normal table for the z-score and subtract it from .5 to obtain the area of a z-score to the mean
If finding the value from the score from the area of the mean which number do you put first?
Your value from the mean of .5000 (or the largest value that you have goes first)
What parts do you know when you use the formula z= (X-u)/o ?
Raw score, the mean, and the standard deviation
What is the simplified version of the z-score formula?
x= u + zo
What are the characteristics of the normal curve?
Any area in a normal curve is distributed in the same way
What does asymptomatic mean?
Curve never actually touches x-axis
What is the proportion of scores?
Anything under normal curve is distributed in the same way
What is the table body in a z-score table?
Represents the area of scores to the left of a respective z-score
What is the first column in a z-table?
First digit of a z-score
What is the first row of in the z-score table?
First two decimal places of a z-score
What are the things you can do with a z-score?
Find area beyond a z-score, find the area between a z-score and the mean, find area between any two z-scores
What happens if you can’t find the exact value?
Pick the larger score to get the smaller proportion
