Binomial Distribution Flashcards
What are the five conditions to be met in order to use a binomial distribution?
- There is a series of N trials
- On each trial, there are only two possible outcomes
- On each trial, the two possible outcomes are mutually exclusive
- There is independence between the outcomes of each trial
- The probability of each possible outcome on any trial stays the same from trial to trial
What is the word that indicates the use of multiplication rule?
And
What is the word that indicates the use of addition rule?
And
The probability of various outcomes of flipping a coin N times can be modeled with ?
Binomial distribution
Each distribution gives two pieces of information: (1) all possible outcomes of the N trials and (2) the probability of getting each of the outcomes.
What is the mathematical expression that allows us to get the number of ways, given N?
Binomial expansion: (P+Q)的N次方 = P^2 + 2PQ+Q^2
P = probability of one of the two possible outcomes of a trial
Q = probability of the other possible outcome
N = number of trials
如果P不等于0.50，the binomial distribution is not symmetrical.
如果P等于0.50, 1) the binomial distribution is symmetrical, 2) it has two tails, it involves a discrete variable, and 3) as N increases, 4) the binomial distribution gets closer to the shape of a normal curve.
Which table does the binomial distribution correspond to?
Table B, up to N = 18 for this course
What is the normal approximation approach? When do we use it?
When the binomial distribution approximates the normal distribution closely enough, we can solve binomial problems using z scores and the normal curve, rather than having to look up many discrete values in a table.
When to use: when NP 大于等于 10 and NQ 大于等于10的时候，用这个方法会比较精确
e.g., :N = 20, P = .50, and Q = .50
or N = 34, P = .30, and Q = .70
or N = 100, P = .10, and Q = .90
Notice that as P and Q get further from .50, N must get larger to meet the criterion.
