Math 10043 Review for Exam 2, Chapters 5, 6, & 7 • Exam Two will have approximately 15 problems. Problem #1 will be true/false, and #2 will be multiple choice covering definitions, properties, and other short-answer kinds of questions. Remaining questions will be mixed up throughout the exam, not necessarily in order by section. •Make sure to show all required work and/or calculator entries! You should write down which calculator command you have used (binompdf, normalcdf, Z-Interval, etc.) and the values you have used as input. NO unsupported answers will be accepted! Formulas and calculator instructions given on the test are on the back of this sheet. •Remember that a probability is a value between 0 and 1 (inclusive). Any problem asking for a probability should be answered to at least 3 decimal places. Some probability problems will require a statement of interpretation. See class notes and answers to Mixed Problems for models of these statements. •Remember that EVERY confidence interval estimate must meet its requirement. Write down both parts – WHAT the requirement is and HOW it is verified. •EVERY confidence interval estimate must end with a CONCLUDING STATEMENT in the context of the problem. This statement should contain enough information to be understandable on its own. •REMEMBER: taking an exam involves making judgments. In order to make good judgments, you need sleep and fuel for your body and brain (i.e. breakfast). Topics covered Ch. 5: Random variables; using and constructing probability distributions; mean and standard deviation of a random variable; probability with a binomial random variable; mean and standard deviation of a binomial random variable. Ch. 6: Finding probability or boundary with the standard normal distribution (i.e., the zdistribution); z notation; finding probability or boundary with any normal distribution; finding µ or σ of a normal distribution using the z-score formula. α Ch. 7: Confidence interval estimates for µ with σ known (with z) – using confidence interval formula and using STAT TEST Z-INTERVAL; finding sample size; CIE for µ with σ unknown (with t) using STAT TEST T-INTERVAL. FORMULAS FOR EXAM 2, Chapters 5, 6 & 7 •Finding a binomial probability: 2nd DISTR [this is the VARS key] binompdf [option 0 or A] enter values for n, p, x ENTER Mean of a binomial random variable: µ = np Standard deviation of a binomial random variable: "= n pq •Finding a probability for a normal distribution: 2nd DISTR [this is the VARS key] ! normalcdf [option 2] enter values for left boundary, right boundary, µ, σ ENTER •Finding a boundary value when you know a probability for a normal distribution: 2nd DISTR [this is the VARS key] invNorm [option 3] enter value for Area to the left of boundary, µ, σ ENTER z-score: z= x !µ ! Confidence interval estimate with z for a population mean µ: Sample size: %z (2 # $ ' " * * n = ' 2 ' * E '& *) ! ! x ± z" 2 # $ n