Binomial distribution

Binompdf

Binompdf

Use for exact probabilities (ex. P(x=5)

Binomcdf

Use for more than, less than, at least, or at most questions

1-binomcdf

Use for “at least” probabilities (ex. P(x≥4); x=3 on Calc)

• Where “x” is AT LEAST a number; not for “no more than” problems

Binomial distribution

B - Binomial; only TWO possible outcomes “success” or failure

I - Independent; the observations are independent; knowing the result of one observation tells you nothing about the others

N - Number; there is a fixed number “n” observations

S - Same probability; the probability of success “p” is the same for each observation

For binomial distribution, we will look at the probability of getting an event with:

n - total number of trials

x - number of successes

p - probability of success

(1-p) - probability of failure

This is the binomial setting

If x is a binomial random variable, it is said to have a binomial distribution, and is denoted as

B(n,p)

If data is produced in a binomial setting, then random variable x is called a

Binomial Random Variable

Binomial coefficient (also called a combination)

The number of ways to arrange x successes in n observations (read as “n choose x)

Math → PRB → 3 nCr

Means are NEVER

Percentages

Population (parameter) mean

µ

Population (parameter) standard deviation

sigma

Population (parameter) proportion

p

Population (parameter) SD of proportion

Sample (statistic) mean

Sample (statistic) standard deviation

Sample (statistic) proportion

Sample (statistic) SD of proportion

Sample Distribution truths

1. The distribution is normal regardless of the shape of the population distribution as long as the sample size, n, is large enough

2. The distribution is normal regardless of the sample size as long as the population distribution is normal

3. The distribution’s mean is the same as the population mean

4. The distribution’s standard deviation is smaller than the population’s standard deviation

Geometric Distribution

1. Only Two outcomes - “success” or failure

2. The probability of success, p, is the same for each observation (consistent probability)

3. n observations are independent

4. TRIALS REPEAT UNTIL YOU GET A SUCCESS

Bins WITHOUT the s - Bint

geometcdf

Use for more than, less than, at least, or at most questions (geometric)

geometpdf

Use for exact probabilities (ex. P(x=5) (geometric)

1-geometcdf

For “at least” problems (geometric)