1. Thank god it’s the Last Friday of february!
Warm-Up…

2. Compare and explain…
your Warm-Up starting with Student #3 at your table (1 min)

7. Mean & standard deviation of a binomial distribution

8. Balance point & spread of 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 that is most commonly used is the standard deviation 
The mean  is the expected value of the number of successes
For the binomial distribution, we can use two special formulas to compute the mean  and the standard deviation 

9. Example:
How do we compute the mean and standard deviation for the distribution that describes the probabilities of lone diners leaving tips?

10. n = 6 p = 0.7 q = 0.3 For the binomial distribution,  = np = 6(0.7)
= 6(0.7)
= 4.2
The balance point of the distribution is at  = 4.2.
The standard deviation is given by

11. Practice

12. Unusual values
Chebyshev’s theorem tells us that no matter what the data distribution looks like, at least 75% of the data will fall within 2 standard deviations of the mean
Data values beyond 2 standard deviations from the mean are less common than those closer to the mean
One indicator that a data value might be an outlier is that it is more than 2.5 standard deviations from the mean

13. Example
Consider a binomial experiment with 20 trials with probability of success being p = 0.70
The expected number of success is  = 14, with a standard deviation of  ≈ 2
What number of successes would be considered unusual?
A number of successes above 19 or below 9 would be unusual

14. Practice