Normal Distribution and Standard Deviation Example
IQ scores are normally distributed with a mean of 100 and a Standard Deviation of 15. We
decide self-proclaimed Smart people are annoying and should be beaten. If we decide to beat
up the 10.03% smartest

Binomial Distributions
o Could it be .8*.8*.8*.8?
o what about her 5th class?
o Could it be .8*.8*.8*.8*.2?
o If THAT looks good, youre on the way!
o BUT .8*.8*.8*.8*.2 is only one of 5 ways she could get 4As and one non-A.
Binomial Distributions are Disc

Characteristics of a Normal Distribution
Given the symmetry of the Graph it is not difficult to comprehend these:
1.The Mode is the high point, the most often occurring value
2.Since the curve is symmetric, for every value a certain distance above the mod

Important Things to Remember about Probability Distribution
1. The VARIANCE of a Probability Distribution is the SUM of cfw_(x minus the MEAN)
SQUARED TIMES the P(x) for each of the pairs. [Standard Deviation is ALWAYS the
positive square root of the vari

Finding Probabilities
To find the probability that z is less than a given value, read the cumulative area in the
table corresponding to that z-score.
Find P( z < -1.24)
Read down the z-column to -1.2 and across to .04 The cumulative area is 0.1075
P ( z <

Continuous Random Variable
Examples:
x = Your weight in a 24 hour period.
o Continuous: your weight is measured
You cannot list all the possible values: 135, 135.1, 135.01, 135.001
x = The EXACT time you got up this morning.
o Continuous: time is measured

Normal Distribution Graph Facts
68.26% of the values will lie within one standard deviation of the mean.
95.44% of the values will lie within two standard deviations of the mean
99.74% of the values will lie within three standard deviations of the mean
CH

Normal Distribution Tables
You may recall we used the AREA in our Uniform Distribution example as a proxy
for PROBABILITY.
Total area was 1 or 1.00 or 100%; probability of a second hand being between 12 and
3 was 25% of the area, hence a probability of .2

Poisson Distribution
o The Poisson distribution is a discrete probability distribution of a random variable, x,
that satisfies the following conditions
o The experiment consists of counting the number of times an event occurs in a given
interval
o The int

Continuous Random Variables
Examples:
x = Your weight in a 24 hour period.
o Continuous: your weight is measured
o You cannot list all the possible values: 135, 135.1, 135.01, 135.001
x = The EXACT time you got up this morning.
o Continuous: time is measu