Ch. 6 Data Analysis and Statistics.
6.1 Combinations and Binomial Theorem.
A. OBJ:
1. to find the number of combinations of r objects
taken from a group of n objects
2. to use Pascal’s triangle to find the number of
combinations
3. to use binomial thm to expand a power of a
binomial sum or difference
B.Facts/Formulas:
1. Combination – selecting r objects from a group of
n objects where the order is not important (nCr)
2. nCr Formula (p.378)
a)
3. Multiple events
a) Event A and (exactly) event B – multiply
b) Event A or (at most) event B – addition
4. Pascal’s Triangle – if you arrange the values of in a
triangular pattern with each row corresponding
to a value of n. (p. 380)
5. Binomial Expansion – relationship between the
powers of the binomial and combinations. (p.
381)
C. Examples:
6.2 Binomial Distribution
A. OBJ:
1. to construct and interpret probability
distributions
2. to classify the distribution as symmetric or
skewed.
B.FACTS:
1. A random variable is a variable whose value is determined
by the outcomes of a random event.
2. A probability distribution is a function that gives the
probability of each possible value of a random variable.
3. A binomial distribution shows the probabilities of the
outcomes of a binomial experiment.
4. A binomial experiment has n independent trials, has only
two outcomes (success or failure) for each trial, and the
probability for success is the same for each trial. nCk * pk * (1p)n-k (p. 389)
5. A probability distribution is symmetric if a vertical line can
be drawn to divide the histogram into two parts that are
mirror images.
6. A distribution that is not symmetric is called skewed.
C. Examples:
6.3 Normal Distributions.
A.OBJ:
1. to use normal distribution to find probability.
2. To use a z-score and the standard table to
calculate probability
B. FACTS/FORMULAS:
1. A normal distribution is modeled by a bell-shaped curve
called a normal curve that is symmetric about the mean.
(curve on p. 399)
2. The standard normal distribution is the normal
distribution with mean 0 and standard deviation The
formula below can be used to transform x-values from a
normal distribution with mean and standard deviation a
into z-values having a standard normal distribution.
z
xx

3. The z-value for a particular x-value is called the z-score for
the x-value and is the number of standard deviations the
x-value lies above or below the mean. (table on p. 401)
C. Examples:
6.4 Sampling.
A.OBJ: to study different sampling methods and
calculate the margin of error.
B.Facts/Formulas:
1. A population is a group of people or objects that
you want information about.
2. A sample is a subset of the population.
a. Self-selected – volunteer
b. Convenience – easy to reach
c. Systematic – a rule is used
d. Random – equal chance of being selected
3. An unbiased sample is representative of the
population you want information about. A
sample that over-represents or underrepresents part of the population is a biased
sample.
4. The margin of error gives a limit on how much
the responses of a sample would differ from the
responses of a population. When a random
sample of size n is taken from a large population,
the margin of error is approximated by this
formula: (p.408)
Margin of error =  1
n
6.5 Comparing Surveys, Experiments and Studies
A. OBJ: to learn how studies are used to collect data
B. FACTS:
1. Survey questions that are flawed in a way that leads to
inaccurate results are called biased questions.
2. An experiment imposes a treatment on individuals in order
to collect data on their response to the treatment.
3. An observational study observes individuals and measures
variables without controlling the individuals or their
environment.
4. In a controlled experiment, two groups are studied under
identical conditions with the exception of one variable. The
group under ordinary conditions is the control group. The
group that is subjected to the treatment is the treatment
group.
5. In a randomized comparative experiment, individuals are
randomly assigned to the control group or the treatment
group