5.4 Binomial Probability Distribution
Objective 3: To determine the exact probability
for x successes in n trials of a binomial
experiment.
Binomial Probability Distribution: a procedure
that meets all the following requirements:
1. the procedure has a fi
5.5 Poisson Distribution
Objective 5: To calculate probabilities for outcomes
of variables using the Poisson distribution.
Poisson Distribution : a discrete probability
distribution that applies to occurrences of some event
over a specified interval. The
6.1 Introduction
Objective 1: To identify distributions as
symmetric or skewed.
Symmetric Distribution: a distribution where
the data values are evenly distributed about the
mean.
Left-Skewed Distribution: the majority of the
data values fall to the right
6.2 Properties of a Normal Distribution
Objective 2: To identify the properties of a
normal distribution.
Recall: In Chapter 5 we dealt with discrete
probability distributions, but in this chapter
continuous probability distributions will be
introduced.
N
6.4 Applications of the Normal Distribution
Objective 4: To calculate probabilities for a
normally distributed variable by transforming it into a
standard normal variable.
Formula to convert data values to z-scores:
z=
x
TI-Nspire Instructions
Menu-Probab
6.5 The Central Limit Theorem
Objective 6: To apply the central limit theorem to
solve problems involving sample means for large
samples.
The sampling distribution of sample means is a
distribution using the means computed from all
possible random samples
6.6 The Normal Approximation to the Binomial
Distribution
Objective 7: To apply the normal approximation to
compute probabilities for a binomial variable.
Recall: Binomial Distribution
1. There must be a fixed number of trials (n).
2. The outcome of each
Chapter 6 Additional Topic
Objective: To calculate probabilities for a
uniformly distributed variable.
Uniform Distribution
A continuous random variable has a
uniform distribution if its values spread
evenly over the range of possibilities. The
graph of a
Probability and Statistics
Chapter 6 Review
1. In a standard normal distribution, find the probability that a z-score:
a. is greater than 1.48
b. is between -1.35 and .77
2. In a standard normal distribution, find the z-score(s) that separate(s):
a. the t
7.3 Confidence Intervals for the Mean (
unknown and n < 30)
Objective 3: To construct the confidence interval for
the mean when is unknown and n < 30.
t Distribution
Similar to the Standard Normal Distribution
Bell-shaped
Symmetric about the mean
Mean,
Probability and Statistics
Review 7.1-7.3
1. Interpret the following 95% confidence interval for mean weekly salaries of shift
managers at Giuseppes Pizza.
$325.80 < < $472.30
2.
Find the sample mean and maximum error for the given confidence interval.
3.
Chapter 7
Confidence Intervals
A 95% confidence interval for the lives (in minutes) of Kodak AA batteries
is 430 < < 470. Assume that this result is based on a sample of size 100.
1. What is the value of the sample mean?
2. What is the value of the sample
7.4 Confidence Intervals and Sample Size for
Proportions
Objective 4: To calculate the confidence interval for
a proportion.
Proportion: can be expressed as a percentage,
decimal, or fraction.
Notation for Proportions
p (population proportion)
p = x/n (sa
7.5 Confidence Intervals for Variances and
Standard Deviations
Objective 6: To construct a confidence interval for a
variance and a standard deviation.
Chi-Square Distribution
Similarities to the t distribution
Involves a family of curves based on the n
Chapter 7 Formulas
x z
< < x + z 2
2
n
n
s
s
x t
< < x + t 2
2
n
n
z
n= 2
E
p z
2
pq
< p < p + z
2
n
z
n = pq 2
E
( n 1) s 2
2 RIGHT
( n 1) s 2
2 RIGHT
2
2
< <
<2 <
( n 1) s 2
2 LEFT
( n 1) s 2
2 LEFT
pq
n
Probability and Statistics
Ch. 7 Review
1. A physical therapist is testing a new technique on patients who are recovering from
sports injuries. To estimate the average length of time she spent with each of these
patients last week, she randomly selected a
8.1 Introduction
Hypothesis Testing: a decision-making process for
evaluating claims about a population.
3 Methods to Test Hypotheses
traditional method: the original method
p-value method: recent method; has become
more popular with increase in technol
8.2 Steps in Hypothesis Testing Traditional
Method
Objective 1: To interpret the definitions used in
hypothesis testing.
There are many definitions highlighted in the notes
for Section 8.2
Objective 2: To state the five steps used in
hypothesis testing.
H
8.3 Z Test for a Mean
Objective 7: To test means for large samples, using
the z test.
Z Test: a statistical test for the mean of a population;
it can be used when n > 30, or when the population is
normally distributed and the population standard
deviation
8.4 T Test for a Mean
Objective 8: To test means for small samples, using
the t test.
T Test: a statistical test for the mean of a population;
it can be used when n < 30, the population standard
deviation is unknown, and the population is normally
distrib
4.1 Introduction
Probability: the chance of an event occurring.
Probability is the basis of inferential statistics.
4.2 Sample Spaces and Probability
Objective 1: To determine sample spaces.
Probability Experiment: a chance process that
leads to well-defi
4.3 Addition Rule
Objective 2: To calculate the probability of
compound events, using the addition rules.
mutually exclusive events: cannot occur at the
same time.
Notation for Addition Rule
P(A or B) = P(event A occurs or event B occurs
or they both occu
4.4 Multiplication Rule
Objective 3: To calculate the probability of
compound events, using the multiplication rules.
Notation for Multiplication Rule
P(A and B) = P(event A occurs in first trial and
event B occurs in second trial)
associate the word and
4.5 Counting Rules
Objective 5: To determine the total number of
outcomes in a sequence of events, using the
fundamental counting rule.
Fundamental Counting Rule: if one event can
occur in m ways and another event can occur n ways,
then the number of ways
4.6 Probability and Counting Rules
Objective 8: To calculate the probability of an
event, using the counting rules.
Examples:
1. Find the probability of obtaining a 7 card hand
all of the same suit from all possible 7 card
hands. (Assume a standard deck o
5.1 Introduction
This chapter explains the concepts and
applications of a probability distribution;
including the binomial and Poisson distributions.
5.2 Probability Distributions
Objective 1: To construct a probability distribution
for a random variable
5.3 Mean, Variance, Standard Deviation, and
Expectation
Objective 2: To calculate the mean, variance,
standard deviation, and expected value for a discrete
random variable.
Mean of a Probability Distribution
also called the expected value
= x P(x)
Varia