Download Math 12 Elementary Statistics Marcella Laddon, Instructor

Math 12 Elementary Statistics
Marcella Laddon, Instructor
Review for Exam 2: Ch. 5 – 6
Reminder: You will be provided the “Formulas and Tables” handout as at the first exam. In addition,
you may bring a 3”x5” index card with any notes you like (both sides). As always, your calculator can
help you with many of the calculations, but it is just a tool. Much of the work can be done from the
tables as well.
Chapter 5 Probability Distributions (note: here we look at discrete distributions)
5.2
Vocabulary here! Have an idea what a probability distribution is all about. How do you know
you’ve got one? Can you construct a probability distribution for a standard 6-sided die? Be able
to calculate the mean, standard deviation, and expected value for a distribution.
5.3
A binomial probability distribution is one particular distribution. Recognize the types of
problems that use the binomial distribution (two outcomes, in particular). Use your calculator to
calculate probabilities (PGRM  BINOM83 or DISTR  binom [know the difference between
the pdf and cdf functions]).
5.4
Be able to find the mean and standard deviation for a binomial distribution and use them to
identify unusual values. Formulas are on the handout I provide.
“Chapter Review”: Read p.246-247, then try Statistical Literacy and Critical Thinking #1 – 3, and
Review Exercises # 1 – 3.
Chapter 6 Normal Probability Distributions (note: here we look at continuous distributions)
6.2
We cannot talk about individual values for a continuous variable, so instead we look at “areas
under a curve.” The total area under such a curve must equal 1. When working with uniform
distributions, probabilities become area of rectangles (base x height). Know that the standard
normal distribution is a bell curve with μ = 0 and σ = 1. We can use “z-scores” when
calculating with the standard normal distribution. Be able to sketch graphs to represent various
probability questions. Be able to find an area/probability given a z-score and to find a z-score
given an area/probability/percentage. You’ll be given the normal table (A-2) in your “Formulas
and Tables” packet, but you can always use your calculator. (DISTRnormalcdf and invNorm;
PGRMNORMAL83 and INVNOR83)
6.3
Solve applications that require the normal distribution with mean & SD other than 0 & 1.
6.4
Think about the difference between a population with its mean ( µ ) and standard deviation ( σ )
and the collection of all possible samples of size n taken from this population. Each sample has
a mean or a proportion. Under certain conditions (section 6.5), this collection or means or
proportions will be normally distributed. In this section, we compute the mean and standard
deviation of the collection of samples the long way – directly from the collection of samples – I
will not ask you to do this on the exam. Do know about biased/unbiased estimators.
6.5
The Central Limit Theorem gives us the conditions under which the collection of sample
means from all possible samples of size n is normally distributed: 1) If the original population is
normally distributed, then so is the collection of sample means. 2) If the original population is
not normally distributed, then a sample size of at least 30 is generally big enough to say that the
collection of sample means is normally distributed. We can then say the mean of our sample
distribution is equal to the population mean (notation: µ x = µ ) and the standard deviation of our
sample distribution is the original SD divided by the square root of n (notation: σ x =
σ
). Note
n
the little x indicating that we’re talking about the collection of sample means, and not the
population. σ x is sometimes called the standard error of the mean. Now we can go ahead and
solve problems involving samples using our techniques of 6.2 and 6.3.
6.6
Review the requirements for a binomial distribution (a discrete distribution). Under certain
conditions (both np and nq must be at least 5), we can use the normal distribution to
approximate the binomial distribution. We use µ = np and σ = npq (as in Chapter 4), and
adjust our x-values up or down by 0.5 as appropriate (drawing a sketch will help you decide –
you always want to include just a little bit more). In particular, this is useful when we have an
interval in a binomial question, not just a particular value.
“Chapter Review”: Read p.320-321, then try Statistical Literacy and Critical Thinking # 1 – 4, and
Review Exercises # 1 - 5.
Probability Distributions
• What are they?
• How do we find the mean and standard
deviation?
• How do we find probabilities?
Discrete Distributions
Binomial
Continuous Distributions
Uniform
Normal
Poisson
Other
Other
The Central Limit Theorem
allows us to use the Normal
Distribution in many situations!