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THE 10 DAYS OF JANUARY – FINAL EXAM REVIEW Day 1: Basic probability, including conditional probability and odds Day 2: Probability of independent and dependent events Day 3: Arithmetic and geometric sequences and series Day 4: Permutations and Combinations Day 5: The binomial theorem Day 6: Binomial probabilities Day 7: Measures of center and dispersion, box and whisker Day 8: Scatterplots Day 9: Sampling and margin of error Day 10: Matrices THE 10 DAYS OF JANUARY – Day 1: Basic probability, including conditional probability and odds 25 students from each grade were randomly selected, and asked to vote for their favorite spirit week activity. Pep Rally Freshmen 12 Sophomore 8 Juniors 7 Seniors 6 A student is selected at random…. Hall Decorating 8 10 9 15 Dance 5 7 9 4 1. P ( Hall Decorating ) 2. P ( Junior ) 3. P ( Freshman or Dance ) 4. P ( Senior and Pep Rally ) 5. P ( Sophomore | Hall Decorating ) 6. P ( Dance | Freshman ) 7. What are the odds in favor of selecting a junior? 8. What are the odds against selecting someone who likes the pep rally? THE 10 DAYS OF JANUARY – Day 2: Probability of independent and dependent events 1. If a coin is tossed and a die is rolled, which is the probability they show heads and an even number? 2. If two cards are drawn from a deck (without replacement), what is the probability they are both hearts? At a health club, 40% of members are female, while 60% are male. Of females, 70% report they have participated in a group exercise class, as opposed to only 35 percent of males. Draw a tree to display these probabilities. 3. What is the probability a health club member is a male, and has participated in an exercise class? 4. What is the probability a random member has participated in a class? THE 10 DAYS OF JANUARY – Day 3: Arithmetic and Geometric Sequences and Series Consider the sequence: (-18), (-15), (-12)… 1. What is the 40th term in the sequence? 2. What is the sum of the first 50 terms in the sequence? A decorative wall is build using rectangular bricks. On the first row of the wall, 200 bricks are used. Each row above this first row uses 2 less bricks than the previous row. 3. How many bricks are there in the 20th row? 4. If the wall has 30 rows, how many bricks are used in total? 8 5. 3n 7 n 1 6. What is the sum of the series: 32 + 16 +8 + 4 + … ? THE 10 DAYS OF JANUARY – Day 4: Permutations and Combinations 1. In how many ways can 4 members from a club with 30 people be chosen to attend a conference? 2. In how many ways can prizes of $50, $25 and $10 be awarded to a group of 12 people? 3. In how many different ways can 9 baseball players be arranged into batting orders? 4. In how many ways can the letters in the word BUBBLES be arranged? 5. 4 cards are randomly selected from a shuffled deck of cards. What is the probability that there are exactly 2 red and 2 black cards drawn from the deck? THE 10 DAYS OF JANUARY – Day 5: The Binomial Theorem 1. Expand - (x 3y)5 2. Expand - (2x y2 )4 3. What is the 3rd term in the expansion of 4. Find and simplify the term in ( x 2 4)7 (x 5y)8 ? which contains x6. THE 10 DAYS OF JANUARY – Day 6: Binomial Probability 60% of goldfish in a large tank (of thousands of fish) are males. A pet store employee reaches into the tank with a scoop and selects 8 of the fish. 1. What is the probability that exactly 5 of the fish are male? 2. What is the probability that 7 or more of the fish are male? 3. 10% of items made at a factory will have a small defect, which causes the item to be adjusted before being sold. In a random sample of 20 items, what is the probability that no more than 2 of the items will have defects? THE 10 DAYS OF JANUARY – Day 7: Measures of Center and Dispersion The graphs below show the average daily wind speeds (in mph) during the last year at two different locations, Dorado Canyon and Nighthwak Valley. 1. Compare the average wind speeds between the two locations. 2. If the average wind speed at Nighthawk is 55mph, would this be considered an outlier? Explain. 3. The standard deviation of the wind speeds at one of these two locations is 4mph. Which location would most likely have this as its standard deviation? 4. Wind speeds at a third location, Wekopa, are normally distributed with a mean wind speed of 25mph, and standard deviation of 8mph. What is the probability a particular day has a wind speed above 33mph? THE 10 DAYS OF JANUARY – Day 8: Scatterplots The scatterplot shown gives the Short Program (SP) and Free Skate (FS) scores for 24 skaters in the 2010 Olympic women’s figure skating competition. 1. Describe the relationship between SP and FS scores. The equation of the best-fit line for this relationship is given by: y 2.07x 16.2 2. If a skater earns a score of 68 in the SP, what is their predicted FS score? 3. An American figure skater generally scores 5 points higher in the Short Program than her teammate. By how many points can we predict she will out-score her teammate in the Free Skate? 4. Give a plausible value for r, given the relationship shown. THE 10 DAYS OF JANUARY – Day 9: Sampling and Margin of Error 1. A newspaper would like to conduct a scientific survey which measures support for using public funds to build a new football stadium. They plan to randomly survey 400 parents at a local youth soccer tournament. Would this be an appropriate survey method? Explain. After conducting an appropriate survey of 400 adults, the newspaper now wants to analyze the results. 2. What is the margin of error of the survey? 3. If 150 of those in the survey agree with using public funds for a new football stadium, then what interval will likely capture the true proportion of those in the population who support the stadium? 4. In order to conduct a survey with a 2% margin of error, approximately how many people should be surveyed? THE 10 DAYS OF JANUARY – Day 10: Matrices 2 3 A 3 2 2 3 C 3 2 5 1 B 4 7 Compute: 1. 2A – 3B 2. AB 3. CD 4. DA 5. Are A and C inverse matrices? How do you know? 1 2 4 D 2 1 6