December 12, FGCU Invitational Mathematics Competition Statistics Team

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2 Directions You will have 4 minutes to answer each question. The scoring will be 16 points for a correct response in the 1 st minute, 12 points for a correct response in the 2 nd minute, 8 points for a correct response in the 3 rd minute, 4 points for a correct response in the 4 th minute. A sliding scale will be used. Once your hand has been raised with the answer sheet, it must stay up. If you put your hand down, your answer will be disqualified for that question. Your answer must be submitted on the official answer sheet that has been correctly filled out. Otherwise your answer will be disqualified. Your answer must be in the specific form that the question asks for. 2

3 Directions If not otherwise noted, the answers should be in one of the following generally accepted forms: Denominators rationalized Simplest radical form Fractions, improper fractions, or mixed numbers in simplest form Equations should have integral coefficients in standard form No units are necessary Calculators are not allowed in any division except Statistics. Headphones, beepers, cell phones, or electronic devices are not permitted. Sunglasses and hats are not to be worn during the competition. 3

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5 Stop Minute 15 Seconds ) As Candy is trying to decide what to wear, she can choose from eight blouses, three skirts and four pairs of shoes. Assuming everything coordinates, how many different possible outfits does she have? 5

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7 Stop Minute 15 Seconds ) Given the data set (x): 21, 19, 32, 10, 5, 7 and 29. If the mean of the data set is A, what is the value of (x-a)? 7

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9 Stop Minute 15 Seconds ) In a pizza restaurant, 95% of the customers order pizza. If 65% of the customers order pizza and a salad, what is the probability that a customer who orders pizza will also order a salad? 9

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11 Stop Minute 15 Seconds ) Lindsay is checking out books at the library. She has narrowed her selections to seven mysteries and eight nonfiction books. If she randomly chooses three books from her selection, what is the probability that there s at least one nonfiction? 11

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13 Stop Minute 15 Seconds ) The national average SAT score (for Verbal and Math) is If the scores have a normal distribution with a population standard deviation of 92, what is the 90 th percentile score? 13

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15 Stop Minute 15 Seconds ) The average monthly mortgage payment including principal and interest is $982 in the U.S. If the standard deviation is approximately $180 and the mortgage payments are normally distributed, what is the probability that a randomly selected monthly payment is more than $1000? (Round the answer to 2 decimals) 15

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17 Stop Minute 15 Seconds ) Listed below are the durations (in hours) of a random sample flights of NASA s Space Transport System (space shuttle). What is the median value?

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19 Stop Minute 15 Seconds ) Suppose Carlos is taking a multiple-choice test where there are five answer choices for each question. If he randomly guesses on four questions, what is the probability that he gets exactly three of those questions correct? (Round the answer to 4 decimals) 19

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21 Stop Minute 15 Seconds ) For a psychology experiment, Emma is assigned the task of finding the mean number of hours students sleep per night. Her results must be at 95% confidence with a maximum error of 0.25 hours. Assuming the standard deviation is 1.5 hours, how many students must Emma survey? 21

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23 Stop Minute 15 Seconds ) Suppose the average size of farms in the U.S. is 443 acres. If the standard deviation is 42 acres, what is the minimum percentage of farms that contained 338 to 548 acres? (Note: the distribution of farm size is not necessarily to be normal.) 23

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25 Stop Minute 15 Seconds ) The correlation coefficient of a linear regression model is What is the amount of variation that is unexplained by the model? 25

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27 Stop Minute 15 Seconds ) The average strawberry has approximately 200 seeds. To test this, a very patient student selected a sample of 10 strawberries and found a sample mean of 190 seeds with a standard deviation of 10. What is the p-value of this test? (Round the answer to 4 decimals) 27

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29 Stop Minute 15 Seconds ) Suppose 55% of customers select a pizza with mushrooms or pepperoni, 32% of customers select only mushrooms, and 17% of customers select only pepperoni. What is the percentage of customers who select both items? 29

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31 Stop Minute 15 Seconds ) The mean length of a random sample of 12 newly hatched iguanas is 7 inches with a standard deviation of 0.75 inches. If the lengths of newly hatched iguanas are normally distributed, what is a 90% confidence interval for the mean length of all newly hatched iguanas? 31

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33 Stop Minute 15 Seconds ) Two samples of size 9 and 13 have variances of 6.5 and 8.5. What is the pooled variance for the two samples? 33

34 Answers 1) 96 2) 0 3) 68.4% 4) 12/13 (or 0.923) 5) ) ) 213 8) ) ) 84% 11) 15.36% or ) ) 6% 14) (6.61, 7.39) 15)