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Algebra II Items to Support Formative Assessment Unit 5: Inferences and Conclusions from Data Summarize, represent, and interpret data on a single count or measurement variable. S.ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. S.ID.A.4 Task Hollywood made quite a few movies in 2011. The estimated production cost of some of the 2011 movies are listed below in millions of dollars. Apollo 18 5 The Ides of March The Roommate 16 Limitless Our Idiot Brother 27 8 Friends With Benefits Bad Teacher 35 20 Midnight in Paris Diary of a Wimpy Kid 2: Rodrick Rules Footloose The Help 17 21 Source Code Bridesmaids 32 32.5 40 27 Horrible Bosses Scream 4 Abduction 35 60 35 Final Destination 5 Spy Kids: All The Time in the World Paul Season Of The Witch Red Riding Hood 25 32 93 95 Johnny English Reborn 45 Super 8 50 The Beaver 79 No Strings Attached The Tree of Life Rise of the Planet of the Apes Zookeeper Rio Hop Gnomeo and Juliet Take Shelter Percy Jackson & The Olympians: The Lightning Thief Never Back Down 2: The Beatdown Twilight: Breaking Dawn Red State 36 71 53 Moneyball 49 Battle: Los Angeles 70 109 The Adjustment Bureau Vanishing on 7th Street Trespass Hesher 48 Immortals 68 57 Mission Impossible 65.5 Mars Needs Moms Dylan Dog: Dead of Night The Big Year The Artist 52.5 51 55 57 Fast Five Kung Fu Panda 2 63 61 Waiting For Forever The Company Men 52.4 75 Take Me Home Tonight The Amazing Mathemelion 72.5 91 54 51 15 12.5 42.5 41 42 Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. 24 25 85 87 63 1. Construct a histogram representing the data above. 2. What can you conclude about Hollywood movie budget (i.e. distribution, mean, standard deviation)? Support your answer using mathematics. 3. You along with your friends Ben and Matt are looking to pitch your original screenplay to a few large Hollywood production companies. You proposed a 74.5 million dollar budget. What percent of movies in 2011 spent less than your proposal? 4. Your original budget proposal of 74.5 million dollars was rejected by production companies. You learned that small indie movies have a better chance of being picked up if 16.6% of the movies cost less than yours to produce. Approximate the movie budget that is appropriate for your movie. Answer: 1. Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. 2. Hollywood movie budget in 2011 is an approximately normal distribution. The mean is approximately 48.67 million dollars and the standard deviation is approximately 24 million dollars. 3. z=1.08, approximately 85.99% of movies cost less than the proposal budget to produce. 4. A proposed budget of 25.39 million dollars will make the movie more likely to be picked up by production companies. Students may work in reserve using the z table to find the corresponding z score then calculate the budget value. S.ID.A.4 Item 1 According to research conducted in 2010, the time that teenagers spend on their phones each day follows a Normal distribution with a mean time of 111 minutes and a standard deviation of 28 minutes. Sue spends an average of 139 minutes on her phone a day. Kendra spends only 55 minutes on her phone each day. Dontrell spends 128 minutes on his phone each day. a. What percentage of teens spend more time than Sue? b. What percentage of teens spend less time on their phones than Kendra does? c. What percentage of teens spend less time on their phones than Dontrell does? Give the zscore as well as the percentage. Answers: a. Using the 68-95-99.7% rule, 16%. b. Using the 68-95-99.7% rule, 2.5%. c. z=0.25, using the z-table 59.87% S.ID.A.4 Item 2 A sample of sandwiches from fast food restaurants was selected and the calories of the sandwiches are represented in the histogram below. The mean number of calories is 450 calories with a standard deviation of 200 calories. Part A Color in all the bars of the histogram that represent the rounded number of calories of a fast food sandwich in the sample that are within 1.5 standard deviations from the mean number of calories of a fast food sandwich. Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. http://mrnussbaum.com/graph/histogram/ Part B Use the histogram to estimate the number of fast food sandwiches in the sample with calories few than 1.5 standard deviations below the mean. Answer: Part A Color in the boxes between 150 and 750. Part B Two sandwiches in this sample had fewer calories than 1.5 standard deviations below the mean. S.ID.A.4 Item 3 You and your partner were assigned to estimate the mean and standard deviation of the Section 6.2 quiz grade distributions for 4 class periods. The grade distributions are represented by the Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. following dot plots. Your partner wants to use the Empirical Rule for all 4 distributions. Do you agree with this approach? Explain your reasoning. Period 1 Period 2 Period 3 Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Period 4 Answer: The Empirical Rule can only be used to estimate mean and standard deviation for approximately normal distributions. The period 4 grade distribution is the only one that can be estimated using the Empirical Rule. S.ID.A.4 Item 4 The distribution of heights of adult American males ages 20 years and over is approximately normal with a mean of 69.3 inches and a standard deviation of 2.5 inches. Part A Draw a normal curve and label the mean and points one, two, and three standard deviations above and below the mean. Part B a. What percent of men are taller than 71.7 inches? b. Between what heights do the middle 95% of men fall? c. What percent of men are shorter than 63 inches? Answers: Part A Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Part B a. Using the empirical rule 68-95-99.7, 16% b. The heights are between 64.3 and 74.3 inches. c. 𝑧 = 63−69.3 2.5 = −2.52; 0.59% of men are shorter than 63 inches. Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.