Probability and the Normal Distribution Flashcards
Define probability:
Measures the likelihood or chance of an event occurring
Equally likely outcomes definition
P(A) = Number of equally likely events in A
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Total number of equally likely events
Why do we use relative frequency
Much more flexible
What are the rules of probability?
Probability of event A, denoted P(A), must be between 0 and 1
P(A)=0 if and only if A is impossible
P(A)=1 if and only if A is certain
What is the addition law?
The addition law states that if two events, A and B, are mutually exclusive (can’t occur simultaneously) then the probability of either event A or event B is
P(A or B) = P(A) + P(B)
What is the multiplication law?
The multiplication law states that if two events, A and B, are independent then the probability of both event A and event B is
P(A and B) = P(A) x P(B)
What is the normal distribution and its equation?
It is a probability density function.
The height of the normal curve with mean μ and standard deviation σ is given by;
Why is the normal distribution important?
Provides a good description of many variables
It is plays a central role in many statistical techniques such as calculating confidence intervals and conducting hypothesis tests
What are the properties of the normal distribution?
Shape dictated by mean and standard deviation
Height of graph dictated by mean
Tails of graph dictated by standard deviation
Area under the curve sums to 1
What is the standard normal distribution?
Values of interest from a Normal distribution often converted to the Standard Normal distribution (referred to as Z-scores)
This is equivalent to counting the number of standard deviations above and below the mean.
Useful as it highlights extreme values
Define relative frequency of probability:
Repeating the experiment a large number of times and noting the proportion of times the event of interest occurs
How do we calculate the area under the curve
Use Excel
Main menu go to Insert > Function then select the function NORMDIST
How do we calculate the value at which a certain proportion of the population lie ?
If we know that a variable is Normally distributed (with a given mean and standard deviation) it is also straightforward to find the value below (or above) which a certain proportion of the population lie
Excel
main menu go to Insert > Function then select the function NORMINV
