STAT1008 Lecture Notes - Lecture 5: Standard Deviation, Confidence Interval, Central Limit Theorem
5 APPROXIMATING WITH A DISTRIBUTION
5.1 NORMAL DISTRIBUTION
Some Bootstrap and Randomization Distributions
Density Curve
- A density curve is a theoretical model to desie a aiale’s distiutio.
- Think of a density curve as an idealized histogram, where:
o (1) The total area under the curve is one.
o (2) The proportion of the population in any interval is the area over that interval.
Normal Distribution
- A normal distribution has a symmetric bell-shaped density
curve
Parameters of a Normal
Two features distinguish one normal density
from another:
- The mean is its ete of set μ.
- The standard deviation controls its spread σ.
- Notatio: X~Nμ,σ
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Example: A Population
Height ~ N(173.25, 10.3)
Ex: Randomization Distribution
Example: Verbal SAT Scores
- Suppose that verbal SAT scores for applicants at a ollege follo a oal distiutio ith ea μ =
ad std. de. σ =.
- What proportion of applicants have SAT scores above 700?
Example: Bootstrap Means
- Suppose that the bootstrap distribution of means for samples of size 500 Atlanta commute times is
N(29.11,0.93).
- Find an endpoint (percentile) so that just 5% of the bootstrap means are smaller.
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Finding Probabilities for N (μ,σ)
Standard Normal
μ=, s= fi )~N,
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Document Summary
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