Test the normal-model approximation
6A–6C
The 68–95–99.7 rule is compared with observed proportions. It is an approximate model statement, not a guaranteed sample result.
Week 2: normal approximation, PDF pp. 33–43
Your task
Calculate your one-SD interval, report its observed share, and judge which distribution is the most plausible normal candidate.
Evidence to include
Use both the shapes and the proportion table rather than a single number near 95%.
Notebook questions and code
Read here; run in your downloaded notebook. Start with its setup cells and run in order. Use your own ID and outputs where requested.
Download Lab 2 notebook6 · When does 68–95–99.7 help? (10 min)
A normal model predicts approximately 68%, 95%, and 99.7% within 1, 2, and 3 SD of its mean. This is not a guarantee for a finite dataset, and symmetry alone is insufficient. We use sample mean/SD here to compare observed proportions with the model.
Python · cell 25 — read here, run in your notebook
rows=[]
for col in ['entry_score','weekly_minutes','assessment_score']:
x=students[col]; m=x.mean(); sd=x.std(ddof=1)
for k in [1,2,3]:
rows.append({'column':col,'SD distance':k,'lower':m-k*sd,'upper':m+k*sd,
'observed %':100*x.between(m-k*sd,m+k*sd).mean(),
'normal model %':{1:68,2:95,3:99.7}[k]})
display(pd.DataFrame(rows))Your reasoning
6A. Give your entry-score interval within 1 SD and observed percentage. Explain why it need not be exactly 68%.
6B. Which column is the most plausible candidate for a normal approximation? Use both shape and proportions. Explain why applying the rule to either of the other columns could mislead.
6C. If an observed proportion happens to be near 95%, has normality been proven? Why not?
Answer: Replace this text with your explanation.
Saved only in this browser. This note doesn’t fill in the downloaded notebook; “reviewed” is a personal checklist, not a grade.