Binomial distribution

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

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

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

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

n - total number of trials

x - number of successes

p - probability of success

(1-p) - probability of failure

This is the binomial setting

B(n,p)

Binomial Random Variable

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

Math → PRB → 3 nCr

Percentages

µ

sigma

p

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

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

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

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

For “at least” problems (geometric)