The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics Review for Midterm Exam 2 3 29 11 review for exam 2 1 Midterm Exam 2 When Thursday 3 31 Where In class Cover Sec 4 1 4 5 5 1 5 2 Format about 30 questions multiple choice closed book calculator needed scantron 3 29 11 review for exam 2 2 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 3 29 11 review for exam 2 3 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 3 29 11 review for exam 2 4 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 3 29 11 review for exam 2 5 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 3 29 11 review for exam 2 6 Some Tips Define events related to the problem of interest Calculate the probabilities by using correct rules Use Venn or tree diagrams 3 29 11 review for exam 2 7 Review of Chapter 5 Q A related to sampling distributions Which statistics count X proportion p or mean X What sample size n What role to play What distribution binomial or normal Which table to use What are the means and standard deviations for those statistics 3 29 11 review for exam 2 8 Sources for Review lecture notes textbook summarize the homework problems you did the practice exam Suggestion problem oriented review 3 29 11 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 3 29 11 review for exam 2 10 Problem 1 continued How many women need to be sampled such that the sample average has its s d smaller than 0 2 Answer n 144 If n women are sampled how likely it is for the sample average to be greater than the population mean P X 0 5 regardless of what values n and take Why 3 29 11 review for exam 2 11 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 3 29 11 review for exam 2 12 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 3 29 11 review for exam 2 13 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 3 29 11 review for exam 2 14 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 3 29 11 review for exam 2 15 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 Hint This is a conditional probability P A B P A and B P B identify A and B and consider the 1st three throws and the last two throws as disjoint blocks so you can use independence 3 29 11 review for exam 2 16
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