Name:Partners: Date: Statistics Review 6 Version A [A] Circle whether each statement is true or false. T F 1. s˛ > s. T F 2. P(z < 1) = .3413 T F 3. Die rolls are approximately normally distributed. T F 4. The score needed to be in the top 60% is the 40th percentile. T F 5. z is the number of standard deviations a score is above the mean. T F 6. 80% of the area under the normal curve is between z ≈ -1.28 and z ≈ 1.28. T F 7. Averages of 30 dice rolled at a time are approximately normally distributed. T F 8. In California, a Trump approval rating above 50% is more likely in a sample of 40 people than in a sample of 80 people. [B] For each problem, find the stated value, shade, approximately to scale, the percentage given in the problem or the percentage representing the answer (but nothing else), and label each boundary of the shaded area with its z score. 1. P(x > 40), given µ = 50 and ß = 10 2. P(x > 40), given µ = 50, ß = 10, and n = 4 3. z, given 95% of the area under the normal curve lies to the left of z 4. z, given 90% of the area under the normal curve lies between -z and z [C] Assume that speeds of cars on Highway 17 in Scotts Valley are normally distributed, with a mean of 68.0 miles per hour and a standard deviation of 5.5 miles per hour. For each problem shade, approximately to scale, the percentage given in the problem or the percentage representing the answer (but nothing else), and label each boundary of the shaded area with its z score. 1. What percentage of cars travel at least 65 mph? 2. How fast is Sarah driving if she is going faster than 95% of the other cars? 3. What is the probability that the next car will be traveling between 65 and 67 mph? 4. What is the probability that the average of the next 9 cars will be between 65 and 67 mph? 5. What range of speeds, centered about the mean, is 90% likely to include the average of the next 9 cars? [D] Do the following to organize your group’s reviews. 1. Make sure your name and your partners’ names are at the top of your review the first day. 2. Staple the reviews in order, all facing the same way. Put the staple in the very top left corner if everyone is finished or if the review is due; otherwise put the staple in the top right corner. Name: Date: Statistics Review 6 Version B [A] Circle whether each statement is true or false. T F 1. s˛ > s. T F 2. P(z < 1) = .3413 T F 3. Die rolls are approximately normally distributed. T F 4. The score needed to be in the top 60% is the 40th percentile. T F 5. z is the number of standard deviations a score is above the mean. T F 6. 80% of the area under the normal curve is between z ≈ -1.28 and z ≈ 1.28. T F 7. Averages of 30 dice rolled at a time are approximately normally distributed. T F 8. In California, a Trump approval rating above 50% is more likely in a sample of 40 people than in a sample of 80 people. [B] For each problem, find the stated value, shade, approximately to scale, the percentage given in the problem or the percentage representing the answer (but nothing else), and label each boundary of the shaded area with its z score. 1. P(x > 40), given µ = 45 and ß = 10 2. P(x > 40), given µ = 45, ß = 10, and n = 6 3. z, given 88% of the area under the normal curve lies to the right of z 4. z, given 90% of the area under the normal curve lies between -z and z [C] Assume that speeds of cars on Highway 17 in Scotts Valley are normally distributed, with a mean of 68.0 miles per hour and a standard deviation of 5.5 miles per hour. For each problem shade, approximately to scale, the percentage given in the problem or the percentage representing the answer (but nothing else), and label each boundary of the shaded area with its z score. 1. What percentage of cars travel at least 66 mph? 2. How fast is Sarah driving if she is going faster than 90% of the other cars? 3. What is the probability that the next car will be traveling between 65 and 70 mph? 4. What is the probability that the average of the next 16 cars will be between 65 and 70 mph? 5. What range of speeds, centered about the mean, is 98% likely to include the average of the next 16 cars? [D] Bonus. 1. Emma measures the speeds of 64 cars on Scotts Valley Drive and finds an average speed of 38 mph with standard deviation 5 mph. Calculate the range, centered about the mean, that has a 90% chance of including the population mean speed. Name: Date: Statistics Review 6 Version C [A] Circle whether each statement is true or false. T F 1. s˛ > s. T F 2. P(z < 1) = .3413 T F 3. Die rolls are approximately normally distributed. T F 4. The score needed to be in the top 60% is the 40th percentile. T F 5. z is the number of standard deviations a score is above the mean. T F 6. 80% of the area under the normal curve is between z ≈ -1.28 and z ≈ 1.28. T F 7. Averages of 30 dice rolled at a time are approximately normally distributed. T F 8. In California, a Trump approval rating above 50% is more likely in a sample of 40 people than in a sample of 80 people. [B] For each problem, find the stated value, shade, approximately to scale, the percentage given in the problem or the percentage representing the answer (but nothing else), and label each boundary of the shaded area with its z score. 1. P(x > 40), given µ = 34.9 and ß = 9.8 2. P(x > 40), given µ = 34.9, ß = 9.8, and n = 6 3. z, given 59% of the area under the normal curve lies to the left of z 4. z, given 99% of the area under the normal curve lies between -z and z [C] Assume that speeds of cars on Highway 17 in Scotts Valley are normally distributed, with a mean of 68.0 miles per hour and a standard deviation of 5.5 miles per hour. For each problem shade, approximately to scale, the percentage given in the problem or the percentage representing the answer (but nothing else), and label each boundary of the shaded area with its z score. 1. What percentage of cars travel at least 67 mph? 2. How fast is Sarah driving if she is going faster than 96% of the other cars? 3. What is the probability that the next car will be traveling between 65 and 66 mph? 4. What is the probability that the average of the next 20 cars will be between 65 and 66 mph? 5. What range of speeds, centered about the mean, is 95% likely to include the average of the next 20 cars? [D] Bonus. 1. Emma measures the speeds of 50 cars on Scotts Valley Drive and finds an average speed of 39.0 mph with standard deviation 4.5 mph. Calculate the range, centered about the mean, that has a 95% chance of including the population mean speed. Name: Date: Statistics Review 6 Version D [A] Circle whether each statement is true or false. T F 1. s˛ > s. T F 2. P(z < 1) = .3413 T F 3. Die rolls are approximately normally distributed. T F 4. The score needed to be in the top 60% is the 40th percentile. T F 5. z is the number of standard deviations a score is above the mean. T F 6. 80% of the area under the normal curve is between z ≈ -1.28 and z ≈ 1.28. T F 7. Averages of 30 dice rolled at a time are approximately normally distributed. T F 8. In California, a Trump approval rating above 50% is more likely in a sample of 40 people than in a sample of 80 people. [B] For each problem, find the stated value, shade, approximately to scale, the percentage given in the problem or the percentage representing the answer (but nothing else), and label each boundary of the shaded area with its z score. 1. P(x > 46), given µ = 45.0 and ß = 3.2 2. P(x > 46), given µ = 45.0, ß = 3.2, and n = 80 3. z, given 99.8% of the area under the normal curve lies to the left of z 4. z, given 99.5% of the area under the normal curve lies between -z and z [C] Assume that speeds of cars on Highway 17 in Scotts Valley are normally distributed, with a mean of 68.0 miles per hour and a standard deviation of 5.5 miles per hour. For each problem shade, approximately to scale, the percentage given in the problem or the percentage representing the answer (but nothing else), and label each boundary of the shaded area with its z score. 1. What percentage of cars travel at least 80 mph? 2. How fast is Sarah driving if she is going faster than 39% of the other cars? 3. What is the probability that the next car will be traveling between 68 and 75 mph? 4. What is the probability that the average of the next 40 cars will be between 68 and 75 mph? 5. What range of speeds, centered about the mean, is 75% likely to include the average of the next 40 cars? [D] Bonus. 1. Emma measures the speeds of 60 cars on Scotts Valley Drive and finds an average speed of 38.0 mph with standard deviation 4.9 mph. Calculate the range, centered about the mean, that has a 99% chance of including the population mean speed.