What is a normal probability distribution?
A distribution of a continuous random variable that is bell-shaped and symmetric around the mean.
Where does the high point of a normal distribution occur?
Over the mean.
What is the relationship between the mean and median in a normal distribution?
They are equal.
What does the empirical rule for normal distributions state?
It gives areas within 1, 2, and 3 standard deviations of the mean.
It is also called the 68-95-99.7 rule
What does a z score measure?
The number of standard deviations a raw score x lies from the mean.
z=(x-mu)/sigma
What is the standard normal distribution characterized by?
It has a mean of 0 and a standard deviation of 1.
What is the purpose of converting raw scores x to z scores?
To use the standard normal distribution table to find probabilities associated with intervals of x values.
True or False: The majority of the area under a normal distribution occurs within 3 standard deviations of the mean.
True
What are normal distributions?
A type of continuous probability distribution characterized by a symmetrical bell-shaped curve
What is a normal curve?
The graphical representation of a normal distribution
How can I find the standard deviation visually?
The standard deviation occurs where it stops being “down life a frown” and starts being up like a sideways smile
What is a normal density function?
A function that describes the probability of a random variable falling within a particular range of values
What is the empirical rule?
A statistical rule stating that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three
What is a z value or z score?
A measure of how many standard deviations an element is from the mean
What are standard units?
Units used to express values in terms of standard deviations from the mean
What is a raw score, x?
The original untransformed score before any standardization
x=z(sigma)+mu
What is the standard normal distribution?
A normal distribution with a mean of 0 and a standard deviation of 1
What does the area under the standard normal curve represent?
The total probability of all outcomes, which equals 1
What are areas under any normal curve used for?
To determine probabilities and percentiles for normally distributed data
