Review Day 2 May 4 th 2013

Probability Events are independent if the outcome of one event does not influence the outcome of any other event Events are mutually exclusive if they cannot occur together. P(A or B) = P(A) + P(B) – P(A and B) If A and B are independent: P(A&B)= P(A)  P(B) P(B|A) = P(A and B)/P(A) The most common way to check for independence is simply to check that P(B) = P(B|A)

Review Questions 1. What is the probability? 2. What is the probability? 3. The two events are 4. What is the probability? 5. What is the probability that exactly one is defective? 1. C2. B3.D4. A5. D

Random Variables

Binomial Distribution

Geometric Distribution

Calculating Geometric Probability

Review Questions P Hint: Binomial Probability 2. Hint: Geometric Probability 3. Hint: Sum of expected sales 4. Hint: Put in L1, L2 (Stat,Cal L1,L2) 5. Hint: To add σ convert to variance Answers: cebea

Free Response P. 183 A. Describe an appropriate model for the number of defective batteries in the shipment. B. What is the mean and standard deviation? C. The consumer group has reason to believe that the rate of defective batteries is at least 5%. Based on your findings in (b), what is the probability that more than 5% of this shipment would be defective if 4% of the manufacturer’s batteries are defective?

The Normal Distribution Symmetric Highest point μ Area under curve = 1 Area on either side of μ is.5 The empirical rule: 68%, 95%, 99.7% Z score measures the distance an observation is from the mean in standard deviations.

Review Questions P Hint: Use Normal Distribution on Calculator. 2. Find the z for top 5%, then find raw score 3. Find both z scores Answers: DAB

Question 4 P. 198 A researcher notes that two populations of lab mice-one consisting of mice with white fur, and one of mice with gray fur-have the same mean weight, and both have approximately normal distributions. However, the population of white mice has a larger standard deviation than the population of gray mice. If the weights for both of these populations were plotted, how would the curves compare to each other?

Question 5 P. 198 Which of the following statements is NOT true for normally distributed data? A. The mean and median are equal B. The area under the curve is dependent upon the mean and standard deviation. C. Almost all of the data lie within 3 σ. D. Approximately 68% of all the data lies within 1 σ. E. When the data are normalized, the distribution has a mean μ = 0, σ = 1

Sampling Distributions Central Limit Theorem for the Mean Central Limit Theorem for Proportion T Distribution Chi Square Distribution

Review Questions P Which of the following statements about the t- distribution is true? 2. The bigger the n, the smaller the σ 3. This is a definition that we had 4. This check for Normality 5. Remember the mean of our sample is the same as our population. The standard deviation divide by square root of n. Answers: becac

Free Response P. 217

Estimation Confidence Intervals: Point estimate ± ME On the AP: statistic ± (critical value)(standard deviation of statistic) Interpreting: a 98% CI indicates that if confidence intervals for all possible samples of size n were constructed for the given population, 98% of the those intervals would contain the population parameter.

Steps for CI 1. Identify parameter 2. Check Conditions 3. Find critical z or t (Perform Calculations) 4. Interpret the results (Context)

Review Questions P c 2. b 3. e 4. d 5. a 6. d 7. a

8. Calculator A 9. B 10. D 11. B 12. C 13. D 14. Calculator won’t work Use formula D 15. A Calculator 2 Prop Z interval

16. Work out by hand 17. D 18. Calculator E (our answer is off b/c DF) 19. B 20. D 21. D 22. C 23. C 24. A