219GUIDEDPROBLEMS6CALC

.pdf

School

University of California, Los Angeles *

*We aren’t endorsed by this school

Course

219

Subject

Mathematics

Date

Jan 9, 2024

Type

pdf

Pages

3

Uploaded by lk3joyce

Report
GUIDED PROBLEMS Chapter 6 • Print (or download) • Complete the work following the guided steps • Scan (if printed), save as a single pdf, and upload to the assignment on MOM or Canvas. NORMAL DISTRIBUITONS Purpose : This guided document depicts the type of work you are expected to show on projects, and the kind of work you need to do to answer test questions. Narrative : Students always ask me if tests are “curved.” Let’s pretend Calculus exams historically followed a normal distribution with a mean of 74.2 percent and a standard deviation of 11.5 percentage points. 1. Empirical rule picture and questions Draw the normal curve for the narrative, with the mean in the middle. Then, mark 1, 2, and 3 standard deviations above and below the mean. Fill in the percentages for the empirical rule based on the 68%, 95%, 99.7% aspect of the rule (all 8 regions need a percentage). Also, place the cut off numbers along the bottom. I put two of them for you. μ -3 s μ -2 s μ - s μ μ + s μ +2 s μ +3 s ____ ___ ____ 74.2 85.7 ____ ____ What percent of Calculus tests have scores higher than 97.2%? (add the percentages above the score of 97.2%) What Calculus test score represents the 84 th percentile? (cut off score such that 84% is the sum of the areas to it’s left)
2. Notation for normal distributions Here is the notation for a random variable, X, being normally distributed with a certain mean and standard deviation. X ~ N( μ , s ) Write the notation for the random variable X in the narrative. Not all normal problems can be answered using the empirical rule. When cut off values or given percentages do not match the empirical rule picture, we need to use “normal methods.” Here are some examples requiring normal methods. 3. What percent of Calculus test scores are between 60% and 90%? Draw Picture: Draw a normal curve with the mean of 74.2 in the middle. Then, draw cut off numbers at 60 and 90, and shade between. This shaded area represents the decimal value of the percentage in question. Show Work: You will need to be able to write the following calculator work before giving the final answer. 1. Pres 2 nd , VARS, select normalcdf. 2. Normalcdf(60, 90, 74.2, 11.5), press enter. Answer: __________% of Calculus test scores are between 60% and 90%.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help