Download CMPT 155 The Normal Distribution

Announcements
 Tuesday, May 2 is our last class
 Final exam review
 Homework 6 2e) will be graded as extra credit
 The last homework (homework 7) is due on Friday,
May 5
 Moodle submission
Normal Distribution
 Both the binomial distribution and the Poisson
distribution describe discrete numerical values.
 The normal distribution provides probabilities for
continuous numerical variables.
 Height of adult males (..., 70, 70.1, 70.12, ...)
 Body temperature (..., 98.6, 98.66, 98.661, ...)
 ...
 Bell-shape curve
 Symmetrical
 Many things closely follow a Normal Distribution:
 Height of adult males
 Body temperature
 Blood pressure
 Marks on a test
 ...
We say the data is "normally
distributed“ if ..
 symmetry about the center
 50% of values less than the mean and 50% greater than
the mean
Measures
 There are two ways to characterize any data
distribution.
 Central tendency: average value
 Dispersion:



how spread out numbers are
how far values in the data set are from the average
standard deviation
The Normal Distribution
 Assume that the height of U.S. males is normally
distributed with an average of 70 inches and with a
standard deviation of 3 inches.
 Generate the normal distribution probabilities for the
height of adult males in one-inch units, including at least 3
standard deviations on each side of the mean.
 Let’s start the spreadsheet!
The NORMDIST() Function
 = NORMDIST(k, μ, σ, cumulative?)
 where
 k is the value of the point of interest (65, 71, ...)
 μ is the average of the distribution (70 inches)
 σ is the standard deviation of the distribution (3
inches)
 and 0 or 1 to indicate whether it is actual probability
or the cumulative probability
Let’s try to answer them:
 What is the proportion of men who are less than 65




inches (including 65) tall?
How about less than 69 (including 69) inches tall?
How about greater than 71 inches tall?
How about greater than 68 inches tall?
What is the proportion of men between 67 and 70
inches tall?
 Attention: Cumulative probabilities must be used
here!
Facts about Normal Distribution
 Approximately 68% of the values lie between +- 1
standard deviation from the average.
 Approximately 95% of the values lie between +- 2
standard deviation from the average.
 Approximately 99% of the values lie between +- 3
standard deviation from the average.

68% of values are within
1 standard deviation of the mean
 \\

95% are within 2 standard deviations

99.7% are within 3 standard deviations
Standard Normal Distribution
 Average μ=0
 Standard deviation σ =1