1. Ten things about Probability
AP Statistics, Second Semester Review

2. Random Variables
A variable that takes on values that are unpredictable in the short term, but form a distribution in the long term.
Random variable can be continuous or discrete

3. Continuous Random Variables: Density Curves
Always non-negative
Area between curve and x-axis equal to one.
Proportion of area above a range of x-values is equal to the probability of the event happening
Famous density curves:
Normal distribution
T-distribution
Chi-square distribution

4. Density Curves Is this a valid density curve? P(0<x<.5)=?

5. Continuous Random Variables
Normal Distributions follow the empirical rule:
Approximately 68% of the distribution is found within 1 standard deviation of the mean
Approximately 95% of the distribution is found within 2 standard deviations of the mean
Approximately 99.7% of the distribution is found within 3 standard deviations of the mean

6. Normal Calculations P(Z<-1)=? P(Z>-1)=? P(0<Z<2)=?
What Z value is associated with being at the 25th percentile?

7. Normal Calculations Let X=N(65.5,2.5) P(X<63)=? P(X>67)=?
What value of X is associated with being a the 75th percentile?

8. Discrete Random Values: Probability Distributions
P(X>3)=?
µx=?
σx=?

9. Binomial Distributions
Binomial Situation: Binary, Independent, Number of trials (n), probability (p) of Success is constant (BINS)
X=the number of successes
X=B(n,p)
Roll a die 10 times, count the number of sixes.
X=B(10,1/6)
Randomly select 100 people and count the number who are left-handed
Y=B(100,.1)

10. Binary Distribution
X=B(10,1/6)
P(X=2)=?
P(X<2)=?
P(X>2)=?

11. Conditional Distributions
P(pierced)=
P(male)=
P(pierced & male)=
P(pierced|male)=
P(male|pierced)=
Are male and pierced independent events?

12. Marginal Distributions
What is the distribution based on gender?
What is the distribution of piercing?

13. Tree Diagrams (Independent Events)
Rolling a “6” and then a “5”

14. Tree Diagrams (Non-independent Events)
4 Brown Socks, 6 Blue Socks

15. Combining Distributions

16. Two rounds of golf
X=N(45,5), Y=N(40,10)

17. Sampling Distribution

18. 5 Women Selected
X=N(65.5,2.5)

19. Sampling Distribution

20. Survey of 500 likely voters
p=.55