Ch 12 - Discrete Probability distributions Flashcards
Binomial distributions are models for
some categorical variables, typically representing the number of successes in a series of n independent trials.
The observations must meet these requirements for a binomial distribution
- the total number of observations n is fixed in advance
- each observation falls into just one of two categories: success and failure
- the outcomes of all n observations are statistically independent
- all n observations have the same probability p of “success”
Binomial distributions describe the
possible number of times that a particular event will occur in a sequence of observations.
We express a binomial distribution
for the count X of successes among n observations as a function of the parameters n and p: B(n,p)
The number of ways of arranging k successes in a series of n observations (with constant probability p of success)
is
the number of possible combinations (unordered sequences).
The binomial probability P(X = k) is
the binomial coefficient multiplied by the probability of any specific arrangement of the k successes
Probability table
The frequency of color blindness (dyschromatopsia) in the Caucasian American male population is estimated to be about 8%. In a group of 25 Caucasian American males, what is the probability that exactly five are color blind?
The center and spread of the binomial distribution for a count X are defined by
the mean m and standard deviation s
binomial probability on calculator
2d - VARS - #A/Bottom
factoral in calculator
MATH - PROB - #4
Effect of changing p when n is fixed
Effect of changing n for a fixed value of p
If _____ the binomial distribution can be approximated by a Normal distribution.
n is large, and p is not too close to 0 or 1,
the Normal approximation can be used when
both np ≥10 and n(1 − p) ≥10.
approximation can be improved by
using a continuity correction to take into account the fact that the Normal distribution is continuous
sample size and normal aprox
