The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Introductory Statistics Review for Midterm Exam 2 10 31 06 review for exam 2 1 Midterm Exam 2 When Thurday 11 2 Where In class Cover Sec 2 1 2 5 4 1 4 5 5 1 only the part for binomial distributions Format 30 questions multiple choice closed book calculator needed scantron 10 31 06 review for exam 2 2 Review of Chapter 2 Scatterplots interpretation Correlation definition and properties Least Squares Regression Find the regression equation prediction and interpretation the meaning of r2 Regression diagnostics Residuals outliers influential observations lurking variables Association vs Causation 10 31 06 review for exam 2 3 Review of Chapter 4 Sample spaces events union intersection complement disjoint events Probability rules addition multiplication Random variables probability distributions means variances rules for means and variances Conditional probability independence Venn and tree diagrams 10 31 06 review for exam 2 4 Probability Rules For any event A P A 1 P not A For any two events A and B P A B P A P B P A B If A B C are disjoint then P A or B or C or P A P B P C Conditional probability P A B P A B P B For any two events A and B P A and B P A P B A P B P A B 10 31 06 review for exam 2 5 Independence Two events A and B are said to be independent if and only if any of the following identities holds one is enough P A B P A P B A P B P A B P A P B Use whichever convenient 10 31 06 review for exam 2 6 combination of rules For any two events A and B P B P B A P B not A P B A P A P B not A P not A Draw a Venn diagram or a tree diagram to see why Bayes rule Don t memorize it but derive it 10 31 06 review for exam 2 7 Some Tips Define events related to the problem of interest Calculate the probabilities by using correct rules Use Venn or tree diagrams 10 31 06 review for exam 2 8 Sources for Review lecture notes textbook summarize the homework problems you did the practice exam Suggestion problem oriented review 10 31 06 review for exam 2 9 Problem 1 The height of American women aged 18 24 can be well approximated by a normal distribution with mean 64 3 in and s d 2 4 in Five women in the age group are randomly selected what s the probability that at least one of them are taller than 66 inches Answer 0 745 10 31 06 review for exam 2 10 Problem 2 An investor has allocated an equal amount of money in two investments Mean returnStandard dev Investment 1 15 25 Investment 2 27 40 Find the expected return of the portfolio 0 21 If the returns on the two investments are independent find the standard deviation of the portfolio 0 2358 10 31 06 review for exam 2 11 Problem 2 continued Redo those parts with the following extensions An unequal allocation of the wealth 1 3 2 3 over the two investments Assuming a correlation 0 1 between returns for the two investments 10 31 06 review for exam 2 12 Problem 3 A lab test yields 2 possible results positive or negative 99 of people with a particular disease will produce a positive result But 2 of people without the disease will also produce a positive result Suppose that 0 1 of the population actually has the disease What is the probability that a person chosen at random will have the disease given that the person s blood yields a positive result 4 7 10 31 06 review for exam 2 13 Problem 4 A Tar Heel basketball player is a 80 free throw shooter Suppose he will shoot 5 free throws during each practice X number of free throws he makes during practice Find the mean and variance of X 4 0 8 10 31 06 review for exam 2 14 Problem 4 continued Given that the player has made more than 2 free throws what is the probability that his 4th and 5th shots are both good 10 31 06 review for exam 2 15