1. The Binomial Distributions
Section 8.1

2. Binomial Setting Each observation falls into one of two categories
Fixed number, n, of observations
n observations are all independent
Probability of success, p, is the same for each observation

3. Binomial Distribution
The distribution of the count X of successes in the binomial setting
Parameters n and p
Possible values of X are the whole numbers from 0 to n.
X is B(n,p)

4. Abbreviations pdf-probability distribution function
cdf-cumulative distribution function

5. Binomial Coefficient
The number of ways of arranging k successes among n observations
Formula on page 447

6. Binomial Probability
Formula for calculating is on page 448

7. Mean and Standard Deviation of a Binomial Random Variable
Mean is equal to the number of observations times the probability of success (np)
Standard Deviation is the square root of the mean times 1 – p
*These formulas only work for binomial distributions

8. Note:
When n is large we can use normal probability calculations to approximate hard to calculate binomial probabilities

9. Rule of Thumb
Use normal approximation when n and p satisfy the conditions that np is greater than or equal to 10 and n(1-p) is greater than or equal to 10

10. Practice Problems
pg. 461 #