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Take-home assignment #4

Data Analysis

Summer 2022

· When an assignment involves working with data or/or coding, you do not need to submit the data or the code that you used to solve the assignment.  You only need to submit your tables, charts, and discussions.

· Your submitted work should all be within one single document that must be either a pdf document or a Word document.  Please note that there are no exceptions to this rule.  That is, assignments that are not in pdf or Word format will not be accepted.  (Please note that “Google”-format documents are not accepted.)

· If the assignment involves creating charts, I suggest you please take a screenshot of your charts and then paste them (one at a time) into a single Word document, and then submit just such single Word document.  (Please recall that we ask that you please submit only one document.)

· Please note that TurnitIn will be used to check for plagiarism of work.  Turnitin checks for plagiarism on documents across all submissions in the class and also submissions from other classes.  It also checks for plagiarism on documents submitted in past classes.

· Please show all your work to receive full credit.  If you provide just the answer, without showing how you derived it, then you will not receive full credit.

1. 
(Chebyshev)  The first row in the table displayed at https://nces.ed.gov/programs/digest/d17/tables/dt17_226.40.asp contains data for the mean and standard deviation for “Total SAT” scores in the U.S. for 2017.  The article at https://blog.prepscholar.com/good-sat-scores-2017 contains data for the 10^th and 90^th percentiles for “Total SAT” scores in the U.S. for 2017.  Please carefully explain if the 10^th and 90^th percentile figures conform with Chebyshev’s theorem.  In other words, please use Chebyshev’s theorem to explain whether the two percentile figures make sense or not.

2. (Chebyshev)  An university collected a sample of data for some of its students regarding their BMI (body mass index).  The BMI is a numerical measure used to infer whether a person is either under-weight, over-weight, or has “regular” weight.  A person with a BMI less than 18 is considered under-weight, a person with a BMI greater than 25 is considered over-weight, and a person with a BMI between 18 and 25 is considered to be with “regular” weight.

The university has the “raw” data, but it releases to you only some “pieces of information” from this raw data.  Specifically, the university tells you that:

a) The sample size is 83

b) The sample average is 21.5

c) A particular student within the dataset has a BMI of 19 and a z-score of –1.25

Based on this information and on Chebyshev’s Theorem, at most how many students within the dataset are either under-weight or over-weight?

Explain and show your work to receive full credit

3. Could the following blue function be a probability density function?  Please explain why or why not.