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ATHSFC– MathDepa artmentAl Ain(2013‐2014) SWQWorrksheet(TeermI) Grade1 11APStatisstics N Name Date S Section Lessons Noormal Distrributions IID Open n the interacttive version of the normaal tables or nnormal distriibution appleet (Opens a separrate browser window) Obtaiin some picttures of norm mal curves. Print P them ouut and use thhem to help ssolve probllems. Exercise E I Part A p time X of jazz CDs C has the normal n distriibution with mean 52 annd standard The playing deviaation 7; the N(52, N 7) distrribution. 1. According g to the 68-9 95-99.7 rule,, what percenntage of jazzz CDs play bbetween 45 and 59 miinutes? 2. What is th he relative frrequency of jazz j CDs wiith playing ttime X less thhan 40 minutes (4 40 minutes is i a typical playing p time for an LP reecord)? Thatt is, find the relative frrequency of the event X < 40. 3. What is th he relative frrequency of jazz j CDs wiith playing ttime X exacttly 45 minutes? 4. What is th he relative frrequency of jazz j CDs wiith playing ttime over 1 hhour? Part B The playing p time X of classiccal CDs has the normal ddistribution w with mean 554 and stand dard deviatio on 5; the N(5 54, 5) distribu ution. 1. A density y curve has 3 important features: f shappe, center annd spread. C Compare eachh of these features fe for th he distributio ons given inn problems 1 and 2. 2. What is the relative frequency of classical CDs with playing time X less than 40 minutes? That is, find the relative frequency of the event X < 40. 3. What relative frequency of classical CDs have playing time over 1 hour? 4. What is the relative frequency of classical CDs with playing time between 45 and 59 minutes? Exercise II SAT (combined) scores of college-bound seniors in high school has the normal distribution with mean 1050 and standard deviation 150. 1. What is the relative frequency college-bound seniors who have SAT score X less than 756? 2. Find the value x such that the 0.025 of all seniors have SAT score below x. (Hint: see part a.). 2.5% of all seniors would have SAT below this value. 3. Find the value x such that the 0.20 of all seniors have SAT score below x. 4. What are the 2.5th and 20th percentiles of this distribution? 5. What is the 97.5th percentile? 6. Use your results to form a 95% probability interval for the SAT score of a college-bound senior. Exercise III A small company records budgeted and actual expenses for each research project it takes on. For instance, a project is budgeted for $100,000; later the actual cost for the project is found to be $103,428. This is a difference of $3,428 or 3.428% over budget (projects finishing under budget are recorded as negatives). You work in accounting where the percentage over/under-budgeted (the "budget discrepancy") has historically been modeled with the normal distribution, mean 1.53% and standard deviation 1.06%. 1. There's a variable X here. Describe X. 2. What is the relative frequency of projects that come in under budget? 3. Find the 99th percentile of budget discrepancies. What percentage of budgets exceed this amount? 4. You examine a year's worth of recent project data: 24 of 498 projects finished with a budget discrepancy over 4%. Does this information agree with the answer of part c?