Algebra 2 Normal Curve Review 1. Describe the features of a normal distribution and explain the 68-95-99.7 rule. 2. Last year, the personal best high jumps of track athletes in a nearby state were normally distributed with a mean of 221 cm and a standard deviation of 11 cm. What is the probability that a randomly selected high jumper had a personal best between 199 and 210 cm? 3. The duration of routine operations in a certain hospital has an approximately normal distribution with an average of 125 minutes and a standard deviation of 15 minutes. What percentage of operations last longer than 155 minutes? 4. Suppose the test scores on an exam show a normal distribution with a mean of 82 and a standard deviation of 5. Within what range do about 95% of the scores fall? About what percent of the scores are between 77 and 92? 5. During boot camp, the drill sergeant measured the weight of the men in his unit. He found the average weight of the men to be 142 pounds and the standard deviation of 14 pounds. The data is normally distributed. Find the interval in which 68% of the data lies. What is the probability that a man picked at random from the unit will weigh more than 170 pounds? What is the probability that he will weigh less than 128 pounds? 6. The number of visits to a gym per year by a sample of 522 members is normally distributed with a mean of 88 and a standard deviation of 19. About how many members went to the gym at least 50 times? What is the probability that a member selected at random went to the gym more than 145 times? 7. The food life of a particular snack chip is normally distributed with a mean of 173.3 days and a standard deviation of 23.6 days. About what percent of the product lasts between 150 and 200 days? About what percent of the product lasts more than 225 days? What range of values represents the outside 5% of the distribution? 8. The insurance industry uses various factors including age, type of car driven, and driving record to determine an individual’s insurance rate. Suppose insurance rates are normally distributed with a mean cost of $829 per person and a standard deviation of $115. What is the range of rates you would expect the middle 68% of the population to pay? If 900 people were sampled, how many would you expect to pay more than $1000? 9. A set of normally distributed tree diameters have a mean of 11.5 cm, standard deviation 2.5 cm, and range from 3.6 cm to 19.8 cm. Monica and Hiroko are to find the range that represents the middle 68% of the data. Is either of them correct? Explain. Monica The data span 16.2 cm. 68% of 16.2 is about 11 cm. Center this 11 cm range around the mean of 11.5 cm. This 68% group will range from about 6 cm to about 17 cm. Hiroko The middle 68% span from ̅ + to ̅ − . So we move 2.5 cm below 11.5 and then 2.5 cm above 11.5. The 68% group will range from 9 cm to 14 cm. 10. A case of portable media players has an average battery life of 8.2 hours with a standard deviation of 0.7 hour. Eight of the players have a battery life greater than 9.3 hours. If the data is normally distributed, how many media players are in the case? Algebra 2 Normal Curve Review For problems 11 – 14, use the data that shows ticket sales of a roller coaster during 10 consecutive hours: 85, 87, 91, 76, 59, 63, 98, 85 11. Find the mean, median, mode, range, and standard deviation of ticket sales. 12. Draw a box and whisker plot for the data 13. If five more tickets were sold each hour, find the mean, median, mode, range, and standard deviation of the new set. 14. The next day twice as many people purchase tickets each hour. Find the mean, median, mode, range, and standard deviation for that day. KEY: 2. 13.5% 3. 2.5% 4. 72 to 92; 81.5% 5. 128 to 156; 2.5%; 16% 6. 0.15% 7. (150 < < 200) ≈ 70% ; ( > 225) ≈ 2%; outside 5% is less than 126.1 and greater than 220.5 8. 68 % from $714 to $944; ( > 1000) ≈ 9.25%; expect about 83 to pay more than $1000 9. Hiroko is correct 10. ( > 9.3) ≈ 9.25%; there are about 87 media players in the case 11. ̅ = 80.5, Median = 85, Mode = 85, Range = 39, ≈ 12.69 13. ̅ = 85.5, Median = 90, Mode = 90, Range = 39, ≈ 12.69 14. ̅ = 161, Median = 170, Mode = 170, Range = 78, ≈ 25.38

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