STA 200 Fall 2009 Name Lab 9Section The purpose of this activity is for you to identify what information is given and what you need to find, and then to compute certain quantities for a normally distributed variable. For questions 1 to 5 and 7 to 9, - draw a normal curve, - label the information given and shade in the area of interest, and- use Table B in your textbook to find the answer. Use the following situation to answer questions 1 to 6.Suppose that a state Board of Education has decided to classify elementary schools according to how well their students do on a new Best Educational Achievement Test. The test will be given to all students in grades 2 through 5. Previous data suggests that the mean for all schools that take the BEAT is 750 with a standard deviation of 50. 1. What percent of the schools will score above 770 on the test?2. What percent of the schools will score between 730 and 800 on the test?3. If your school scores 780 on the test, your school did better than what percent of all schools taking the test?4. Schools that score in the top 20% are labeled excellent. What score does a school need to be labeled excellent?5. Schools in the bottom 25% are labeled "in danger". What score does a school need to be labeled “in danger”? 6. The Board of Education wants a nice graphic to use when explaining these test scores to the public. They’d like a picture that would show people where there school scored in relation to other schools. Draw a normal curve that shows the intervals of test scores into which 68%, 95%, and 99.7% of the test scores fall.Use the following situation to answer questions 7 to 9.A machine at a factory fills “16-ounce” cans of coffee. The fill amounts (in ounces) are approximately normally distribution with a standard deviation of 0.52 ounces. The supervisor chooses the mean fill level and can change that amount at any time.7. Suppose the fill level is set so that the average can holds 16 ounces. In one day 4,000 cans are filled. How many of those cans hold less than 15 ounces? 8. Suppose the fill level is set so that the average can holds 16.2 ounces. What percent of cans are over-filled (hold more than 16 ounces)?9. At what level should the mean fill amount be set, so that only 5% of the cans are under-filled (have less than 16 ounces)?Use the following situation to answer questions 10 to 12.According to the data about U.S. Presidents’ ages at inauguration, themean age at inauguration is 54.8 with a standard deviation of 6.2. 10. Assuming that this data is normally distributed, use the empirical rule to find the interval into which we expect 95% of the ages to fall. 11. List the inauguration ages for any president beyond 2 standard deviations from the mean (in either direction). Identify these presidents by name (see list on the next page).12. a) How many presidents’ inauguration ages fall within 2 standard deviations of the mean? b) What percent of the inauguration ages are within 2 standard deviations of the mean? c) Is this close to what you would expect based on the empirical rule?Presidents of the United StatesPresidentAge atInaugu-rationAge atDeathWashington 57 67J. Adams 61 90Jefferson 57 83Madison 57 85Monroe 58 73J.Q. Adams 57 80Jackson 61 78Van Buren 54 79W.H. Harrison 68 68Tyler 51 71Polk 49 53Taylor 64 65Fillmore 50 74Pierce 48 64Buchanan 65 77Lincoln 52 56A. Johnson 56 66Grant 46 63Hayes 54 70Garfield 49 49Arthur 50 57Cleveland 47 71B. Harrison 55 67(Cleveland) 55 71McKinley 54 58PresidentAge atInaugu-rationAge atDeathT. Roosevelt 42 60Taft 51 72Wilson 56 67Harding 55 57Coolidge 51 60Hoover 54 90F.D. Roosevelt 51 63Truman 60 88Eisenhower 62 79Kennedy 43 46L. Johnson 55 64Nixon 56 81Ford 61Carter 52Reagan 69 93G.H. Bush 64Clinton 46G.W. Bush