AP STATISTICS Name Chapter 6 Applications Period: Use summary statistics to answer the question. Solve the problem.

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1 AP STATISTICS Chapter 6 Applications Name Period: Use summary statistics to answer the question. 1) The speed vehicles travelled on a local highway was recorded for one month. The speeds ranged from 48 mph to 63 mph with a mean speed of 57 mph and a standard deviation of 8 mph. The quartiles and median speeds were 51 mph, 60 mph, and 54 mph. Is the distribution symmetric, skewed to the left, or skewed to the right? Explain. 2) Here are some statistics for the annual Wildcat golf tournament: lowest score = 57, mean score = 97, median = 105, range =108, IQR = 99, Q1 = 39, standard deviation = 15. Suppose it was very windy and all the golfers' scores went up by 7 strokes. Tell the new value for each of the summary statistics. A) Lowest score: 64, mean: 97, median: 105, range: 115, IQR: 99, Q1: 46, SD: 15 B) Lowest score: 64, mean: 104, median: 112, range: 108, IQR: 99, Q1: 46, SD: 15 C) Lowest score: 64, mean: 104, median: 112, range: 115, IQR: 106, Q1: 46, SD: 15 D) Lowest score: 64, mean: 104, median: 112, range: 115, IQR: 99, Q1: 46, SD: 22 E) Lowest score: 64, mean: 104, median: 112, range: 115, IQR: 99, Q1: 46, SD: 15 3) The test scores from a recent Mathematics test are as follows: 95.5, 65.9, 93.2, 88.6, 56.8, 50, 86.4, 54.5, 40.9, 77.3, 79.5, 65.9, 70.5, 77.3, 81.8, 50, 79.5, and The mean score was 71.2 with a standard deviation of If the Normal model is appropriate, what percent of the scores will be less than 40.2? Round to the nearest tenth. 4) For a recent English exam, use the Normal model N(73, 9.2) to find the score that represents the 90th percentile. 5) A bank's loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, what percentage can be expected to be between 200 and 275? 6) For a recent English exam, use the Normal model N(73, 9.2) to find the percent of scores between 56 and 87. Round to the nearest tenth of a percent. 1

2 7) The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume less than 32 oz? 8) For a recent English exam, use the Normal model N(73, 9.2) to find the percent of scores over 85. Round to the nearest tenth of a percent. 9) For a recent English exam, use the Normal model N(73, 9.2) to find the percent of scores under 58. Round to the nearest tenth of a percent. Draw the Normal model and use the Rule to answer the question. 10) Assuming a Normal model applies, a town's average annual snowfall (in inches) is modeled by N(48, 9). Draw and label the Normal model. About what percent represents snowfall of less than 57 inches? 11) The mean weights for medium navel oranges is 9.8 ounces. Suppose that the standard deviation for the oranges is 3.3 ounces. Which would be more likely, an orange weighing 14 ounces or an orange weighing 4.9 ounces? Explain. 12) On a recent English exam, scores averaged 76 points. If 2% of scores fell above 95 points, find an approximate standard deviation (assuming the Normal model is appropriate). Round to the nearest tenth. 13) For a recent English exam, use the Normal model N(73, 9.2) to find the score that represents the 30th percentile. 2

3 Draw the Normal model and use the Rule to answer the question. 14) An English instructor gave a final exam and found a mean score of 65 points and a standard deviation of 6.3 points. Assume that a Normal model can be applied. Draw and label the Normal model for the exam scores. What percent of scores should be between 77.6 and 83.9 points? 15) After increased patrol, 91% of vehicles on an old town highway travel above 45 mph with a standard deviation of 5.8. Assuming a Normal model is appropriate, find the mean speed. Use summary statistics to answer the question. 16) A local ice cream shop hand scoops each of its ice cream cones. The cones vary in weight from 4.6 ounces to 7.3 ounces with a mean of 6.45 ounces and a standard deviation of 1.2 ounces. The quartiles and median weights are 5.6, 9.1, and 7.2 ounces. Is the distribution symmetric, skewed to the left, or skewed to the right? Explain. Round to the nearest tenth. 17) Based on the Normal model for snowfall in a certain town N(57, 8), how many inches of snow would represent the 75th percentile? 18) Based on the Normal model for car speeds on an old town highway N(77, 9.1), what is the cutoff value for the lowest 30% of the speeds? 19) The average number of babies born in Ellensurg each year is 267 with a standard deviation of 29. How many standard deviations from the mean is a year with 385 babies born? 3

4 20) A town's average snowfall is 48 inches per year with a standard deviation of 6 inches. Using a Normal model, what values should border the middle 68% of the model? 21) A basketball coach kept stats for his team in free throw percentage and steals (among others). At the last game, Erin's free throw percentage was 79% and she had 4 steals. The team averaged 95% from the free throw line with a standard deviation of 15 and they averaged 7 steals with a standard deviation of 4. In which category did Erin do better compared with her team? Explain. 22) On a recent English exam, if 94% of scores fell above 65 points and the standard deviation is 6.9, find the mean score (assuming the Normal model is appropriate). 23) The average size of forest fires last year was 853 acres with a standard deviation of 106 acres. How many standard deviations from the mean is a forest fire consuming 253 acres? 24) After increased patrol, 33% of vehicles on an old town highway travel below 45 mph with a standard deviation of 5.8. Assuming a Normal model is appropriate, find the mean speed. 25) The average number of days absent per student per year at West Valley School is 19 days with a standard deviation of 4 days. How many standard deviations from the mean is of 3 absent days? 4

5 Answer Key Testname: CHAPTER 6 APPLICATION 1) Skewed to the right, mean higher than median. 2) B 3) 2.5% 4) ) 43.32% 6) 90.4% 7) 40.13% 8) 9.7% 9) 5.2% 10) Snowfall (in.) ; 84% 11) A 14 ounce orange is more likely (z = 1.27) compared with an orange weighing 4.9 ounces (z = -1.48). 12) ) ) Exam Score ; 2.35% 15) mph 16) Skewed to the left, mean lower than median. 17) 62.4 inches 18) about 72.3 mph 19) About 4.07 standard deviations above the mean 20) 54 inches and 42 inches 21) Steals. 4 steals is from the mean. 22) ) About 5.66 standard deviations below the mean 24) mph 25) About 4.00 standard deviations below the mean 16 standard deviations from the mean while 79% free throw average is - standard deviations 15 5