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AP Statistics Chapter Two Review Part 1 1. The best male long jumpers for State College since 1973 have averaged a jump of 263.0 inches with a standard deviation of 14.0 inches. The best female long jumpers have averaged 201.2 inches with a standard deviation of 7.7 inches. This year, Joey jumped 275 inches and his sister, Carla, jumped 207 inches. Both are State College students. Assume that the lengths of jumps for both males and females are approximately normal. Within their groups, which athlete had the more impressive performance? Write complete sentences explaining your reasoning. Show all calculations. The Empirical Rule In a normal distribution with mean µ and standard deviation σ : Approximately ________ percent of the observations fall within one σ of the mean. Approximately ________ percent of the observations fall within 2σ of the mean. Approximately ________ percent of the observations fall within 3σ of the mean. 2. Let z denote a random variable having a standard normal distribution. Determine each of the following probabilities. (1 point each) You may use the chart or your calculator. a) P (z < 1.28) b) P (z < - 1.05) c) P (z > - 2.51) d) P (- 1.30 < z < 1.54) e) What is the value of z for the 65th percentile? f) What is the value of z* on the graph that separates the middle 92% as shown below. In other words, the area of the shaded region is 0.92. What is the value of z*? AP Statistics Chapter 2 Review Part 1 3. In the accompanying display below, which normal curve has the larger mean? ________ (1 point) In the accompanying display below , which normal curve has the larger standard deviation? ________ 4. A gasoline tank for a certain model car is designed to hold 12 gallons of gas. Suppose that the actual capacity of the gas tank in cars of this type is well approximated by a normal distribution with mean 12.0 gallons and standard deviation 0.2 gallons. What is the probability that a randomly selected car of this model will have a gas tank that holds at most 11.7 gallons? Use good notation and show all work. 5. The time that it takes a randomly selected employee to perform a certain task is approximately normally distributed with a mean value of 120 seconds and a standard deviation of 20 seconds. The slowest 10% (that is, the 10% with the longest times) are to be given remedial training. What times qualify for the remedial training? AP Statistics Chapter 2 Review Part 1 1. The best male long jumpers for State College since 1973 have averaged a jump of 263.0 inches with a standard deviation of 14.0 inches. The best female long jumpers have averaged 201.2 inches with a standard deviation of 7.7 inches. This year, Joey jumped 275 inches and his sister, Carla, jumped 207 inches. Both are State College students. Assume that the lengths of jumps for both males and females are approximately normal. Within their groups, which athlete had the more impressive performance? Write complete sentences explaining your reasoning. Show all calculations. ( 5 points) zm = 275 − 263 ≈ .8571 14 zf = 207 − 201.2 ≈ .7532 7.7 Joey had a more impressive long jump since he is .8571 standard deviations away from the mean compared to .7532 for Carla. The Empirical Rule In a normal distribution with mean µ and standard deviation σ : Approximately ________ percent of the observations fall within one σ of the mean. Approximately ________ percent of the observations fall within 2σ of the mean. Approximately ________ percent of the observations fall within 3σ of the mean. 2. Let z denote a random variable having a standard normal distribution. Determine each of the following probabilities. (1 point each) You may use the chart or your calculator. a) P (z < 1.28) b) P (z < - 1.05) c) P (z > - 2.51) d) P (- 1.30 < z < 1.54) e) What is the value of z for the 65th percentile? AP Statistics Chapter 2 Review Part 1 f) What is the value of z* on the graph that separates the middle 92% as shown below. In other words, the area of the shaded region is 0.92. What is the value of z*? 5. In the accompanying display below, which normal curve has the larger mean? ________ (1 point) In the accompanying display below , which normal curve has the larger standard deviation? ________ (1 point) 6. A gasoline tank for a certain model car is designed to hold 12 gallons of gas. Suppose that the actual capacity of the gas tank in cars of this type is well approximated by a normal distribution with mean 12.0 gallons and standard deviation 0.2 gallons. What is the probability that a randomly selected car of this model will have a gas tank that holds at most 11.7 gallons? Use good notation and show all work. (4 points) 5. The time that it takes a randomly selected employee to perform a certain task is approximately normally distributed with a mean value of 120 seconds and a standard deviation of 20 seconds. The slowest 10% (that is, the 10% with the longest times) are to be given remedial training. What times qualify for the remedial training? (4 points)