Download 2.1 Density Curves and Normal Distributions density curve

2.1 Density Curves and Normal Distributions
density curve:
describes overall pattern of a distribution
area under the curve is one
mean ( µ ) - balance point (goes towards the long
tail of a skewed distribution)
standard deviation ( σ )
median divides the area in half (equal-areas pt)
simulation: allows you to quickly get a distribution
*calculator: randint
68 – 95 – 99.7% Rule (Empirical Rule)
68% of the data of a normal distribution lies
within one standard deviation of the mean.
95% of the data of a normal distribution lies
within two standard deviations of the mean.
99.7% of the data of a normal distribution lies
within three standard deviations of the mean.
ex. µ = 32 , σ = 5 Sketch a density curve
The distribution of scores on Mr. Metz’s exam
had a mean of 75 and a standard deviation of 4.
Assume a normal distribution and answer the
following:
a) In what range do the middle 95% of scores
lie?
b) What percent of students scored above a
79?
c) What percent of students scored below a
67?
d) What percentile does a score of 83 place
you in?
e) What percentile does a score of 71 place
you in?
f) What percentile does a score of 67 place
you in?