Business Statistics Ch. 5

Front 1

discrete data definition

Back 1

values are whole numbers (integers);
usually counted, not measured
Examples: # of complaints per day, # of TVs in a household, # of rings before the phone is answered

Front 2

continuous data definition

Back 2

can potentially take on any value, depending only on the ability to measure accurately;
often measured, fractional values are possible;
examples: thickness of an item, time required to complete a task, temperature of a solution, height, in inches

Front 3

discrete probability distribution graph

Back 3

Front 4

continuous probability distribution graph

Back 4

Front 5

discrete random variables definition

Back 5

have outcomes that typically take on whole numbers as a result of conducting an experiment;
finite number of values

Front 6

continuous random variables definition

Back 6

have outcomes that take on any numerical value as a result of conducting an experiment;
infinite number of outcomes;
examples:
length of time a customer waits in a checkout line
weight of a tractor-trailor at a weight station

Front 7

a discrete probability distribution is...

Back 7

a listing of all the possible outcomes of an experiment for a discrete random variable;
along with the relative frequency of each outcome

Front 8

A discrete probability distribution meets the following conditions:

Back 8

1. each outcome in the distribution needs to be mutually exclusive with other outcomes in the distribution
2. the probability of each outcome, P(x), must be between 0 and 1
3. the sum of the probabilities for all the outcomes int he distribution must be 1

Front 9

The mean, μ, of a discrete probability distribution...

Back 9

is the weighted average of the outcomes of the random variables that comprise it;
Also known as the espected value, E(x)

μ = The mean of the discrete probability distribution
xi = The value of the random variable for the ith outcome
P(xi) = The probability that the ith outcome will occur
n = The number of outcomes in the distribution

Front 10

Variance of a discrete probability distribution...

Back 10

is a measure of the spread of the individual values around the mean of a data set;

Front 11

formula for the variance of a discrete probability distribution

Back 11

σ^2 = The variance of the discrete probability distribution
xi = The value of the random variable for the ith outcome
μ = The mean of the discrete probability distribution
P(xi) = The probability that the ith outcome will occur
n = The number of outcomes in the distribution

Front 12

expected monetary value (EMV) definition

Back 12

the mean of a discrete probability distribution when the discrete random variable is expressed in terms of dollars;
the EMV represents a long-term average, as if outcomes from the distribution occurred many times

Front 13

characteristics of binomial distributions

Back 13

1. experiment consists of a fixed # of trials, denoted by n
2. each trial has only 2 possible outcomes, a success or failure
3. the probability of a success p and the probability of a failure q are constant throughout the experiment
4. each trial is independent of the other trials in the experiment

Front 14

examples of binomial distributions

Back 14

a survey response to a question is yes or no;
an electronic component is either defective or acceptable;
new job applicants either accept an offer or reject it

Front 15

Binomial distributions formula

Back 15

P(x,n) = The probability of observing x successes in n trials
n = Number of trials
x = Number of successes
p = Probability of a success
q = Probability of a failure

Front 16

formula for calculating the mean of a binomial distribution

Back 16

μ = The mean of the binomial distribution
σ = The standard deviation of the binomial distribution
n = The number of trials
p = The probability of a success
q = The probability of a failure

Front 17

formula for calculating the standard deviation of a binomial distribution

Back 17

μ = The mean of the binomial distribution
σ = The standard deviation of the binomial distribution
n = The number of trials
p = The probability of a success
q = The probability of a failure

Front 18

Poisson distribution...

Back 18

is useful for calculating the probability that a certain number of events will occur over a specific interval of time or space;
examples: # of customers per hour, # of flaws per meter of cloth, # of accidents per month

Front 19

Characteristics of a poisson process

Back 19

1. experiment consists of counting the number (x) of occurrences of an event over a period of time, area, distance, or other type of measurement
2. the mean (λ) has to be the same for each equal interval of measurement
3. the # of occurrences during one interval has to be independent of the number of occurrences in any other interval
4. the intervals defined in the poisson process cannot overlap

Front 20

formula for the Poisson probability distribution

Back 20

x = The number of occurrences of interest over the interval
λ = The mean number of occurrences over the interval
e = 2.71828
P(x) = The probability of exactly x occurrences over the interval

Front 21

formula for the variance of a Poisson distribution

Back 21

the variance of the distribution is the same as the mean

Front 22

what is a common use of the Poisson distribution?

Back 22

to determine the probability of customer arrivals

Front 23

Binomial probabilities can be calculated using the Poisson distribution when the following conditions are present:

Back 23

when the # of trials, n, is greater than or equal to 20

AND

when the probability of a success, p, is less than or equal to 0.05

Front 24

formula for using the poisson equation to calculate binomial probabilities

Back 24