AP Stats Review of old material 1. Name___________________________ Lefties are definitely out-numbered, considering that they make up only 10% of the population. If you randomly select 200 students, what is the probability that at least 24 of them are left-handed? 2. Only 2% of the population have green eyes. In a school of 2000 students a. How many do you expect to find with green eyes? b. What is the probability that exactly 48 have green eyes? c. What is the probability that at least 42 have green eyes? d. What is the probability that less than 35 have green eyes? 3. A study at a university found that 26 children out of a group of 150 children ages 2 to 9 were obese. Calculate a 95% confidence interval for the true proportion of children (from 2 to 9) who are obese. 4. The average weight of a yorkie is 6 pounds with a standard deviation of 0.72 pounds. If we randomly select 300 yorkies, what is the probability that the mean weigh is at least 8 pounds? 5. There is a 13% failure rate for algebra 1. You are interviewing students about their courses. Find the probability that the you don’t find a student who failed algebra 1 until the fifth interview. 6. In a survey, students were asked how many hours they sleep each night. A sample of 28 students had a mean sleep time of 6.8 hours with a standard deviation of 1.24 hours. Construct and interpret a 90% confidence interval for the mean number of hours slept per night for students. 7. We want to estimate the mean ACT scores for students in the south. A sample of 50 southern students had a mean score of 20.8. Construct and interpret a 95% confidence interval for the mean ACT score if the standard deviation for the ACT is known to be 4.8 points. 8. The eights of ten college basketball players are shown below. Construct and interpret a 98% confidence interval for the mean height of college basketball players. 72 84 76 74 81 72 73 74 79 75 9. What is meant by the 98% level in problem #8? 10. Find the mean and standard deviation of the following: x p(x) 5 0.24 8 0.18 12 0.11 18 0.08 22 26 0.21 11. I want to estimate the mean IQ score within 5 points for students in AP courses using a 95% confidence interval. How large of a sample will I need if the standard deviation is known to be 15 points? 12. I want to estimate the proportion of people with dimples in their chins. How many will I need to sample if I want to be within 5% of the true proportion using a 90% confidence interval?