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P Distributions
3.14 NCEA level 3 statistics
Question | Answer |
---|---|
What are the two parameters of normal distribution? | Mean and the standard deviation |
How can you calculate a rough standard deviation? | Divide the overall range by 6 (because 99% of the data is within three standard deviations from the mean) |
What are the features of a Normal distribution model? | Unimodal, Symmetrical, Bell shaped, and unbounded |
What are the proportions of a normal distribution probability model? | The area under the curve is equal to one 68% of normally distributed data is within one standard deviation of the mean 95% is within two standard deviations of the mean 99% is within 3 std Devs |
What equation is needed for a conditional normal distribution problem? | P(A l B) = P(A n B) / P(B) |
For rectangle distribution how do calculate the height of the rectangle? | The height of the rectangle is just one over the length. |
When should you use a rectangular distribution model? | When the only information you are given is maximum and minimum values |
What are the properties of a uniform distribution? | Continuous Has a minimum and maximum value Each value is equally likely to occur The probability of obtaining a range of values = area under the graph for those values |
When should you use a triangular distribution model? | When the only information you are given is a maximum, minimum and an average/mode. Usually used for continuous data |
How to calculate area of triangle? | Half base times height |
How to calculate are of rectangle? | Bases times height |
λ meaning? | The mean number of occurrences per continuous period |
What does Crispy fish stand for? | Conditions:R events must occur at random and the rate at which the event occurs is constant I events must be independent S events cannot occur simultaneously P probability of an event occurring is proportional to the size of the continuous interval |
What is the one parameter of Poisson distributions? | λ - Average number of successes or rate of successes |
When doing inverse Poisson problems, if X=0 then what happens to the equation? | Goes from P(X=x)=e-λλx/x! to P(X=0)=e-λ |
What does Bi nom I al stand for? | Bi: There are only two outcomes (success, failure) Nom: There is a fixed number of trials (n) I: Each trial is independent, the outcome of one trial does not affect the outcome of another Al: The probability of each success is constant |
What are the two parameters of a binomial distribution? | n - the number of trials π - the probability of success for each trial |