1. Additional Properties of the Binomial Distribution
Skill 25

2. Objectives Compute  and  for a binomial distribution.
Compute the minimum number of trials n needed to achieve a given probability of success P (r).

3. Mean and Standard Deviation of a Binomial Distribution
Two other features that help describe the graph of any distribution are the balance point of the distribution and the spread of the distribution about that balance point.
The balance point is the mean  of the distribution, and the measure of spread is the standard deviation .
The mean  is the expected value of the number of successes.

4. Mean and Standard Deviation of a Binomial Distribution
For the binomial distribution, we can use two special formulas to compute the mean  and the standard deviation .

6. Example–Compute  and 
A waiter at the Green Spot Restaurant has learned from long experience that the probability that a lone diner will leave a tip is only 0.7.
During one lunch hour, the waiter serves six people who are dining by themselves.
Compute the mean and standard deviation.

7. Example–Compute  and 
n = p = q = 0.3
For the binomial distribution,
 = np = 6(0.7) = 4.2
The balance point of the distribution is at  = 4.2

8. Example–Solution
The standard deviation is given by

9. Example–Riverside Basketball
The Riverside basketball team has 75% chance of winning a game. During this coming season Riverside has 9 games before Christmas break.
Find the probability of the Riverside basketball team winning exactly 7 games before Christmas breaks.

10. Example–Riverside Basketball
Find n, p, q, and r.
Find Probability of the Riverside basketball team winning exactly 7 games before break.

11. Example–Riverside Basketball
Find Probability of the Riverside basketball team winning 7 or more games before break.

12. Example–Riverside Basketball
Find the balance point and standard deviation.

13. Pick the Right Formula…
Discrete Distribution
- More than 2 possibilities
*Use 5.1 Formulas*
Binomial Distribution
- 2 possibilities
*Use 5.2/5.3 Formulas*

14. 25: Additional Properties of the Binomial Distribution
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