Ch 11 - Bayes' theorem & Normal Distribution Flashcards
Normal—or Gaussian—distributions are
a family of symmetrical, bell-shaped density curves defined by a mean m (mu) and a standard deviation s (sigma): N(m,s).
Normal distrabution inflection point
Normal curves are used to
model many biological variables. They can describe a population distribution or a probability distribution .
Normal Curve means vs SD
Good candidate for a normal model
All normal curves N(µ,σ) share the same properties
About 68% of all observations are within 1 standard deviation (s) of the mean (m).
About 95% of all observations are within 2 s of the mean m.
Almost all (99.7%) observations are within 3 s of the mean.
What % have low or very low
We can standardize data by
computing a z-score
A z-score measures
the number of standard deviations that a data value x is from the mean m.
When x is 1 standard deviation larger than the mean, then z =
When x is 2 standard deviations larger than the mean, then z =
When x is larger than the mean, z is
positive.
When x is smaller than the mean, z is
negative.
Table B gives
the area under the standard Normal curve to the left of any z-value.
two ways of finding the area under N(0,1) curve to the right of a z-value.
To calculate the area between two z-values
first get the area under N(0,1) to the left for each z-value from Table B.
Then subtract the smaller area from the larger area.
Don’t subtract the z-values!!! Normal curves are not square!
he area under N(0,1) for a single value of z is
zero
because area under a point is a line which is zero
(need a range)
Inverse normal calculations
find probability from z score
The lengths of pregnancies, when malnourished mothers are given vitamins and better food, is approximately N(266, 15). How long are the 75% longest pregnancies in this population?
way to assess if a data set has an approximately Normal distribution is to
plot the data on a Normal quantile plot.
Cannot do by hand - use technology
1) The data points are ranked and the percentile ranks are converted to z-scores.
2) The z-scores are then used for the horizontal axis and the actual data values are used for the vertical axis.
3) If the data have approximately a Normal distribution, the Normal quantile plot will have roughly a straight-line pattern.
