Stats Exam 2 - Terms 4,5,6

conditional probability

probability of event A given B has occured

The ____________ mean is the appropriate measure to use when evaluating growth rates.

geometric

Trimmed mean

Same as the mean except omit highest and lowest k% of data values (e.g., %) =TRIMMEAN(Data, Percent)

Subjective

Based on informed opinion or judgement

Classical

Known a priori by the nature of the experiement

Mean absolute deviation (MAD)

This statistic reveals the average distance from the center. Absolute values must be used since otherwise the deviations around the mean would be zero. =AVEDEV(Data)

Binomial distribution

a binomial random variable X is the sum of n independent Bernoulli random variables

Tree diagrams

a diagram used to display events and probabilities to help visualize all possible outcomes.

discrete probability distributions

assigns probability to each value of a discrete random variable X.

Which of the following event are mutually exclusive? a. Being of German decent and being of Mexican decent. b. Passing a statistics test and passing an English test c. Rolling an odd number and an even number on the same roll of the die. d. Being on time and being late for an appointment.

c. Rolling an odd number and an even number on the same roll of the die. and d. Being on time and being late for an appointment.

The ________ formula is used to determine the number of different ways to arrange a group of x objects from a total of n objects and the other order of the objects is irrelevant.

combination

For any given event, the sum of the probability of that event and the probability of its ____________ must equal one.

complement

simple event

or elementary event is a single outcome

Subjective approch

reflects informed judgement about the likelihood of an event. This method is needed when there is no repeatable random experiment.

Bimodal or Multimodal

distribution occurs when dissimilar populations are combined into one sample.

True or false: Chebyshev's Theorem should only be applied to data sets that are normally distributed.

false

True or false: The geometric mean does not mitigate the effect of outliers.

false

Special law of multiplication

if events A and B are independent then P(A and B) = P(A)P(B)

Outlier (z-score classification)

if the absolute value of z1>3 (beyond u +/- 3o)

Collectively exhaustive

if their union is the entire sample space S (all the events that could possibly occur)

Population variance (sigma squared)

Sum of the squared deviations from the mean divided by the population size.

Unusual (z-score classification)

if absolute value of z1>2 (beyond u +/- 2o)

Independence

look at conditional probabilities to determine independence

Nadia purchased 400 shares of XYZ stock at $20 per share. When the stock decreased in value to $16 a share, Nadia purchased 600 more shares of XYZ stock. The weighted average price per share that Nadia paid for XYZ stock is $_____ (use 2 decimal places).

$17.60

Quartiles

(denoted Q1, Q2, Q3) are scale points that divided the sorted data into four groups of approximately equal size, that is, the 25th, 50th, and 75th percentile respectively

Calculate the standardized score for the following data value. Assume the mean = 100 and the standard deviation = 25: x=60, z=_____.

-1.6

An apartment complex rents an average of 2.3 new units per week. If the number of apartments rented each week has a Poisson distribution, then the probability of renting exactly three apartments in a week is __________ [round your answer to 3 decimal places and do not enter a percentage]

.203 (e^-2.3)(2.3^3)/3! = 0.203

A company received an average of .64 purchase orders per minute. Assuming a Poisson distribution for the number of purchase order per minute, what is the standard deviation for this distribution? a. 1.28 b. 2 c. 0.8 d. 0.41

.8 [The standard deviation is the square of the mean in a Poisson distribution.]

XYZ Corp. has filled 100,000 purchase order during its existence. 1,100 of the purchase orders have had errors. Using empirical probability, the probability of the next purchase order having an error is __________ (round your answer to three decimal place and enter as a probability not a percentage).

0.011 1100/100,000 = 0.011

The odds against a horse winning a race were set at 7 to 1. The probability of that horse not winning the race is ___________ . Answer should be in decimal form, using 3 decimal places.

0.875 (7/1+7)= 0.875

A list of the top twenty restaurants in Chicago was released. Four of the restaurants specialize in seafood. If five restaurants are selected randomly from the list, the expected value for the number of restaurants specializing in seafood is _______________.

1

Match the following terms with their meaning: 1. Mesokuric 2. Platykurtic 3. Leptokurtic ___A flatter distribution than normal with heavier tails __ Normal bell-shaped distribution -- A sharply peaked distribution with thinner tails

1. Mesokutic is normal bell-shaped distribution 2. Platykurtic is a flatter distribution than normal with heavier tails 3. Leptokirtic is sharply peaked distribution with thinner tails

A random variable X has μ = 25 and σ = 5. A new random variable Y = 5X. The mean of Y is ____________.

125 5(25) = 125

Mike is placing a bet on an upcoming horse race in which 7 horses are running. Mike places a trifecta bet that wins only if he correctly picks the first, second, and third place horses in order. There are _________ possible outcomes for the first three horses in the correct order.

210 [permutation] nPr= n! ------ (n-r)!

A company sold 1000 units in its first year of operation, 1400 units in its second year of operation, and 1680 units in the third year of operation. The average growth rate of the company's sale for years one to three is ______%. (round your final answer to a decimal answer with four places and then convert to % with 2 decimals)

29.61% square root of (1680/1000) - 1 = 0.2961

In general, a data point is considered an outlier if it falls more than ________ standard deviations away from the average.

3

Quartile divide the data into _______ (choose a number) of equal parts

4

20% of a restaurant's customers order the chef's special. 230 customers are anticipated to dine tonight at the restaurant. The expected number of chef's specials that will be ordered tonight is ______________.

46 230 x 0.2 = 46

Suppose 20% of a business's employees commute by bus. How many employees will have to be sampled in order to find the first employee who commutes by bus?

5 1/.2 = 5

If the median price for a home is $200,000, than _______% of homes cost less than $200,000.

50

For the data set 4,5,6, and 9 the arithmetic mean is

6

The range for the data set: 2, 5, 5, 7, and 10 is _____________.

8

The empirical rule states that approximately ________% of observations will fall within two standard deviations of the mean.

95.44%

Binomial shape

A binomial distribution is skewed right if Pi<.50 and skewed left if Pi>.50 and symmetric only if Pi=.50 Use =BINOM.DIST(x, n, pi, cumulative)

Sample correlation coefficient

A well-know statistic that describes the degree of linearity between paired observations on two quantitative variable X and Y

Empirical approach / relative frequency approach

Counting the frequency of observed outcomes (f) defined in our experimental sample space and dividing by the number of observations (n). The estimated probability if f/n.

PDF - probability distribution function

Defined by either a list of X-values and their probabilites or by mathematical equations. A discrete PDF shows the probability of each X-value

Independent

Each occurrence has no effect on the probability of the other events occuring

Special law of addition

If A and B are exclusive events then the general addition law can be simplified to the sum of the individual probabilities for A and B

Venn diagram

Illustration of A' and A

Recognizing hyper-geometric application

Look for a finite population (N) containing a known number of successes (s) and sampling without replacement (n items in the sample) where the probability of success is not constant for each sample item drawn.

Covariance

Measures the degree to which the values of X and Y change together.

Median

Middle value in sorted array =MEDIAN(data)

Mode

Most frequently occurring data value. =MODE.SNGL(data)

The five nines rule

Prime business customers expect public carrier-class telecommunications data links to be available 99.999% or the times. This equates to 5 min downtime per year.

Standardized date

Redefine each observation in terms of its distance from the mean in standard deviations

Excel quartiles

Q1: =QUARTILE.EXC(Data 1) (25% below) Q2 =QUARTILE.EXC(Data2) (50% below) Q3 =QUARTILE.EXC(Data3) (75% below)

Fine the first and third quartiles from the following data set using the method of medians: 2, 3, 3, 5, 6, 8, 12.

Q1=3, Q3=8

z-score

Standardized values that can tell us how far away from the mean each observation lies

CDF - cumulative distribution distribution function

The CDF shows the cumulative sum of probabilities, adding from the smallest to the largest X-value.

Law of Large Numbers

The as the number of trials increases any empirical probability approaches its theoretical limit.

Range (R)

The difference between the largest and smallest observations. =MAX(Data)-MIN(Data)

Intersection

The event consisting of all outcomes in the sample space S that are contained in both event A and B.

Symmetric data

The mean and median are about the same. Tails of the histogram are balanced (low/high values offset) mean [almost equals] median

Skewed right (positively skewed)

The mean exceeds the median. Long tail of histogram points right (most data on left but a few high values) Mean>Median

Poisson distribution (model of rare events)

The number of occurrences within a randomly chosen unit of time or space. All characteristics are determined by its mean λ. The standard divination of the square root is its mean.

Joint Probability

The probability A and B

Kurtosis

The relative length of the tails and the degree of concentration in the center

Coefficient of variation

The standard deviation expressed as a percent of the mean.

Mean

The statistical measure of center. Sum of the data values divided by the number of data items. =AVERAGE(data)

True or false: υ^2 represents the variance

True

classical approach

Using deduction to determine probability

Which of the following are characteristics of a binomial distribution? a. Each trial is independent of the previous trail b. Each trail has only two possible outcomes c. It is continuous distribution d. For each trail the probability of success remains the same

a. Each trial is independent of the previous trail and b. Each trail has only two possible outcomes and d. For each trail the probability of success remains the same

Generally, a negative covariance between market demands indicated [check all the apply] a. a centralized distribution will decrease the aggregate demand variance b. a centralized distribution center can reduce the need for safety stock c. a centralized distribution center will decrease the aggregate average demand d. a centralized distribution center will increase the need for safety stock.

a. a centralized distribution will decrease the aggregate demand variance and b. a centralized distribution center can reduce the need for safety stock

Which of the following are characteristics of the geometric distribution? [check all that apply] a. counts the number of trial until the first success b. the mean is 2/π c. the probability of success is not constant d. a series of Bernoulli trials

a. counts the number of trial until the first success and d. a series of Bernoulli trials

A binomial distribution is skewed left when the probability of success is a. greater than .5 b. less than .5 c. equal to .5

a. greater than .5

The interquartile range of a data set: (check all that apply) a. is calculated by subtracting the first quartile from the third quartile b. represents the middle 75% of the data c. is the range between the first and fourth quartiles d. represents the middle 50% of the data

a. is calculated by subtracting the first quartile from the third quartile and d. represents the middle 50% of the data

A company receives an average of 0.8 purchase orders per minute. The company wants to determine the probability of receiving 6 purchase orders in 5 minutes. What value should she company use for the mean to help calculate the probability? a. 6 b. 4 c. 5 d. 0.8

b. 4

Which of the following experiments is likely to produce a uniform discrete distribution? a. Test scores on college entrance exam, such as the ACT or SAT b. The answer selected on a multiple choice question that has four choices by a student who did not study c. The values that occur from repeated spins of a roulette wheel at a casino d. The number of patrons arriving every 3 minutes at a sandwich shop.

b. The answer selected on a multiple choice question that has four choices by a student who did not study [the student would be guessing so each answer is equally likely.] and c. The values that occur from repeated spins of a roulette wheel at a casino

How many outcomes of an experiment constitute a simple event? a. more than one b. one c. two d. none

b. one

A box plot is constructed using several different values. Which of the following values from a data set are included in a box plot? a. the fifth quartile b. the largest value c. the first quartile d. the mean e. the mode

b. the largest value and c. the first quartile

One common way to describe a Poisson process is a. the model of departure times. b. the model of arrivals c. the model of dependent events

b. the model of arrivals

Which of the following random variables meets the criteria for a hyper-geometric distribution? a. The average number of adults who have a graduate degree is 0.7/household. Let X be the number of adults in a household who have a graduate degree. b. Suppose 30% of the population have a graduate degree. Define X to be the number of adults in a sample of 20 who have earned a graduate degree. c. Out of 50 adults, 10 who have a graduate degree. A sample of 20 is taken. Define X to be the number of adults in the sample with a graduate degree.

c. Out of 50 adults, 10 who have a graduate degree. A sample of 20 is taken. Define X to be the number of adults in the sample with a graduate degree.

Which of the following should one look for when identifying a hyper-geometric application? [check all the apply] a. probability of success is constant b. sampling with replacement c. a known number of success s d. a finite population N

c. a known number of success s and d. a finite population N

Redundancy

can increase system reliability even when individual component reliability is low

A festival has become so popular that it must limit the number of tickets it issues. People who hope to attend the festival send in a request for tickets, and requests are filled by random selection. Only 21% of the ticket requests are fulfilled. what are the odds of not receiving a ticket for a random applicant? a. 3.34 to 1 b. 3.88 to 1 c. 2.98 to 1 d. 3.76 to 1

d. 3.76 to 1 1-0.21/0.21 = 3.76

Which of the following is not an example of an experiment? a. Picking a team that will wine the World Series b.Buying a computer base on repair history. c. Selecting a care from a deck of cards. d. Pick the team that won last year's World Series.

d. Pick the team that won last year's World Series.

Using the multiplication rule, the joint probability of even A and event B is computed by multiplying the conditional probability of event A given event B by the probability of: a. event B given event A b. event A c. the union of A and B d. event B

d. event B

5!=? a. 25 b. 24 c. 100 d. 5 e. 120

e. 120 A factorial is the product of all number from 1 to n. Therefore 5! = 5*4*3*2*1 = 120

Emperical

estimated from observed outcome frequnecy

Actuarial science

estimating empirical probabilities

Independent events

event A is independent of event B if and only if P(A/B)=P(A)

Complement (A')

everything in the sample space S except event A

Percentile

ex. 83rd percentile means 83% of the test takers are below you

Events that cannot occur at the same time are mutually ________ events.

exclusive

Method of medians

for small data sets, you can fine quartiles this way. 1. sort observations 2. find the median Q 3. find the median of the data values that lie below Q 4. find the median of the data values that lie above Q2

random variable

function or rule that assigns a numerical value to each outcome in the sample space of a random experiment

The _______ mean is the multiplicative average of the data set.

geometric

discrete random variable

has a countable number of distinct values. Some random variable have a clear upper limit and others do not

actuarially fair

insurance program must collect as much overall revenue as it pays out in claims. Premiums must be set to reflect empirical experience with the insured group.

The _____________ of two events A and B contains only those outcomes that are in both A and B.

intersection

event

is any subset of outcomes in the sample space

a compound event

is expressed using an inequality.

Variance Var(X) of a discrete random diviation

is the sum of the squared deviation about its expected value, weighted by the probability of each X-value.

Weighted mean

is the sum that assigned each data value a weight w1 that represents a fraction of the total (i.e. the k weights must sum to 1)

Expected value E(X)

is the weighted average that measures center, the variance

Empirical Rule says that data from a normal data distribution, we expect the interval u +/- ko to contain a known percentage of the data:

k=1 68.26% will lie within u +/- 1o k=2 95.44% will line within u+/- 2o k=3 99.73 % will line within u+/- 3o

The measure of center where half the values of the data set lie above this measure and half the values of the data set lie below this measure is known as the

median

Bayes Theorem

method of revising probabilities to reflect new information. Prior (unconditional) probability of an event B is revised after event A has occurred to yield a posterior (conditional) probability.

The _________ is the measure of the center that identifies the most frequently occurring value in the data set.

mode

Binary events

mutually exclusive collectively exaustive

Mesokurtic

normal bell shaped population

Leptokurtic

peaked more sharply than normal

The set of all possible outcomes from a random experiment is called a _________ __________.

sample space

hyper-geometric distribution

similar to the binomial except that sampling is without replacement from a finite population of N items. Therefore the trails are not independent and the porbability of success is not constant from trial to trail.

A probability assigned by a person that is based on that person's judgement or experience is a ___________ probability.

subjective

The mean of a Bernoulli distribution is π, called the probability of ___________.

success

The expected value of the sum of two or more random variables is equal to the _________ of their individual values.

sum

probability

the number of measure the relative likelihood that the event will occur. P(A)

General law of addition

the probability of the union of two events A and B is the sum of their probabilities less the probability of their intersection

True or false: The arithmetic mean is the average of a data set.

true

When a data set is symmetrical the mean and the median are approximately

the same

Mutually exclusive

their intersection is the empty set (contains no elements). One event precluded the other from occurring.

The mode for the data set: 4, 5, 6, 9 is

there is no mode

Union

two events consist fo all outcomes in the sample that are contained in wither A or B or both

compound event

two or some simple events

A prior probability for event A is the ____________ probability whereas the posterior probability of event A is the ___________ probability.

unconditional conditional

Box plots

useful for EDA (exploratory data analysis) - center (position of the median Q2). This plot shows varaibility (width of the box) defined by Q1 and Q3 and the range between xmin and xmax. A box plot shows shape

Multiplying data by a fraction (where the fractions add to 1) and summing results in a _____ mean.

weighted

Uniform distribution

One of the simplest discrete models. It describes a random variable with a finite number of consecutive integer values from a to b. The entire distribution depends on only two parameters.

The median for the data set 10, 6, 4, 9, 5 is

6

20% of a restaurants customers order the chef's special. 230 customers are anticipated to dine at the restaurant tonight. The STANDARD DEVIATION for this binomial distribution is _____________ (round your answer to 3 decimal places)

6.066 230 x 0.2 x 0.8 = 36.8 square root of 36.8 = 6.066

Platykurtic

A population that is flatter than normal

Recognizing a Poisson application

-occurs randomly over time or space -average arrival rate remains constant -arrivals are independent of each other -The random variable X is the number of event within an observed time interval

The following table represents the number of cartons of milk that childrenat Hoover-Wood Elementary school purchase for lunch. Milk Probability 0 .2 1 .7 2 3+ .02 The probability that a student purchases 2 milk cartons is ____________.

.08

The average number of customers arriving at Jimmy's Burgers is 1.7 per minute. What is the probability that only 1 customer arrives in the next minute? ______________ (Round to three decimals and do not enter a percentage.)

.311 1.7^1e^-1.7/1! = .311

Professor Stats has 40 students in her statistics class. 24 of the students are male. If she randomly selects 6 of her students at, without replacement, the probability of selecting 4 men in the sample is _________ [round your answer to three decimal places.)

.332

The maximum value of a data set is 200 and the minimum value is 80. The midrange is equal to ____________.

140

sample space

The set of all possible outcomes (S) for the experiment

True or false: E(X)=u

True

When estimating sigma using the following formula: Xmax-Xmin/6, one is assuming the distribution is: a. normal b. highly skewed c. Bimodal d. No assumption on the distribution

a. normal

The box plot is constructed using several different values. Which of the following values from a data set are included in a box plot? a. the largest value b. the mean c. the mode d. the first quartile e. the fifth quartile

a. the largest value and d. the first quartile

A box plot is constructed using several different values. Which of the following values are included in a box plot? (select all that apply) a. the smallest value b. the standard deviation c. the 90th percentile d. the second quartile e. the third quartile

a. the smallest value d. the second quartile e. the third quartile

Define event A = {1, 2, 3, 4} and event B = {2, 3, 6, 7}. A or B = a. {1, 2, 3, 4, 6, 7} b. 5 c. {1, 4, 6, 7} d. {2, 3}

a. {1, 2, 3, 4, 6, 7}

The following relative frequencies help determine if residents' location affects whether the residents get season passes to the pool on the west side. E W Total Pass 0.3 0.45 0.75 None 0.15 0.10 0.25 Total 0.45 0.55 1.0 a. 0.55 b. 0.1 c. 0.15 d. 0.45

b. 0.1

Calculate the joint probability that a country club member plays tennis and golf. Ten. No Total G. 180 0 0 no 0 50 100 Totals 230 400 a. 0.25 b. 0.45 c. 0.125 d. 0.575

b. 0.45

Consider rolling two dice. Which of the following describe two events that are collectively exhaustive? [select all that apply] a. Event 1: A value of 9 or more. Event 2: A value of 7 or less. b. Event 1: rolling an even number. Event 2: Rolling an odd number c. Event 1: A value of 7 or more. Event 2: A value of 6 or less. d. Event 1: A value of 6 or more. Event 2: A value of 8 or less

b. Event 1: rolling an even number. Event 2: Rolling an odd number and c. Event 1: A value of 7 or more. Event 2: A value of 6 or less. and d. Event 1: A value of 6 or more. Event 2: A value of 8 or less

The following contingency table can help determine if residents' location is independent of whether or not the resident purchases a season pass to the pool. The pool is located on the West side. East West Total Pass 35 50 85 None 25 10 35 60 60 120 a. P(pass and East) and P(none) b. P(Pass and East)P(pass) c. P(pass and West)P(pass) d. P(pass and West) and P(East)

b. P(Pass and East)P(pass) and c. P(pass and West)P(pass)

The following contingency table can help determine if residents' location is independent of whether or not the resident purchases a season pass to the pool. [The pool is located on the West side.] East West Total SPass 35 50 85 NPass 25 10 35 Total 60 60 120 Which comparison of probabilities would you choose to show dependence between a resident's location and whether or not they purchased a season pass? a. P(Season pass and lives West) and P(Lives East) b. P(Season pass/Lives West) P(Season Pass) c. P(Season Pass/Lives East) P(Season Pass) d. P(Season Pass and Lives East) and P(no Season Pass)

b. P(Season pass/Lives West) P(Season Pass) and c. P(Season Pass/Lives East) P(Season Pass)

contingency table

cross-tabulations of frequencies

Compound events

cumulative probabilities can be evaluated by summing individual X probabilities.

Calculate the marginal probability that a country club member plays tennis. T No T Totals G 180 No G 50 100 Totals 230 400 a. 0.25 b. 0.125 c. 0.45 d. 0.575

d. 0.575 230/400 = 0.575

Calculate the conditional probability that a country club member plays golf given that they play tennis. T No T Total G 180 No G 50 100 Total 230 400 a. 0.5 b. 0.45 c. 0.125 d. 0.783

d. 0.783

The sum of the probabilities of all the outcomes in the sample space is: a. Impossible to determine without more information b. 0 (zero) c. 0.5 (one half) d. 1 (one)

d. 1 (one)

The correlation coefficient describes the degree of ______ between two ________ variables. a. nonlinearity; qualitative b. nolinearity; quantitative c. linearity; qualitative d. linearity; quantitative

d. linearity; quantitative

A numerical value that measures the likelihood of an uncertain even occurring is a ________________.

probability

Marginal probabilites

probability of an event relative to the frequency that is found by dividing a row or column total by the total sample size

True or false: The trimmed mean can mitigate the effect of outliers.

true

Kareem is trying to decide which college to attend full time next year. Kareem believes there is a 55% chance that he will attend State College and a 33% change that he will attend Northern University. The probability that Kereem will attend either State or Northern is _________ [state your answer as a decimal and round your answer to two decimal places.]

0.88

Suppose a data set has 80 data points. A 5% trimmed mean would be calculated by removing the ___________ highest values and the __________ lowest values.

4 4

Midrange)

=0.5*(MIN(Data)+MAX(Data))

Geometric mean (G)

=GEOMEAN(Data)

Sample standard deviation (s)

=STDEV.S(Data)

Standard deviation

=STDEV.S(Data)

Sample variance (s^2)

=VAR.S(Data)

Variance

=VAR.S(Data)

If Fund A has a coefficient of 1.1 and Fund B has a coefficient of variation of 0.9, Fund ____ has the greater relative dispersion.

A

Bernoulli experiment

A random experiment that has only two outcomes.

random experiment

An observational process whose results cannot be known in advance

A tree diagram has ___________ probabilities at the terminal end of each branch.

conditional

Interquartile range

The first and third quartiles Q1 and Q3 indicate the center because they define the boundaries for the middle 50% of the data, but Q1 and Q3 also indicate variability because the interquartile range Q3-Q1 (IQR) measure the degree of spread in the data (middle 50%)

Skewed left (negatively skewed)

The mean is below the median. Long tail of histogram points left (a few low values but most data on right) Mean<median

The average number of customers arriving at Jimmy's Burgers in a minute is 1.7. Which expression would one use to calculate the probability that at least 4 customers arrive in a randomly chosen minute? a. 1-P(X</=3) b. P(C</=3) c. 1-P(X</=4) d. P(X>4)

a. 1-P(X</=3)

Consider rolling two dice. Which of the following describe two events that are collectively exhaustive? a. Event 1 A value of 7 or more. Event 2: A value of 6 or less b. Event 1: A value of 9 or more. Event 2: A value of 7 or less c. Event 1: A value of 6 or more. Event 2: A value of 8 or less d. Event 1: rolling an even number. Event 2: Rolling an odd number

a. Event 1: A value of 7 or more. Event 2: A value of 6 or less [Their union included all possible outcomes of rolling two dice] and c. Event 1: A value of 6 or more. Event 2: A value of 8 or less [The union includes all possible outcomes of rolling two dice] and d. Event 1: rolling an even number. Event 2: Rolling an odd number [Their union includes all possible outcomes of rolling two dice]

Which expression(s) below would be correct for calculating the probability that no more than 2 of 4 patients has health insurance? [check that apply] a. P(X </= 2) b. P(X < 2) c. P(X = 0)+P(X = 1)+P(X = 2) d. P(X = 2)+P(X = 3)+P(X = 4)

a. P(X </= 2) and c. P(X = 0)+P(X = 1)+P(X = 2)

In which of the following ways are binomial distributions and hyper-geometric distributions similar? [check all that apply] a. They both have two possible outcomes: success or failure b. They are both discrete distributions c. They both assume each trial is independent of each other. d. The probability of success is constant in each trail.

a. They both have two possible outcomes: success or failure and b. They are both discrete distributions

The binomial distribution can be approximated using the Poisson [check all that apply] a. When n is large and π is less than or equal to .05 b. if n < 10 and π > .5 c. by letting λ = nπ d. when n is small and π is large

a. When n is large and π is less than or equal to .05 and c. by letting λ = nπ

Discrete random variables: [check all that apply] a. have a set of distinct values b. are countable c. can have a finite or infinite number of values d. must have a clear upper limit

a. have a set of distinct values and b. are countable and c. can have a finite or infinite number of values

The probability of State College winning a football game is 0.6. The probability of University of State winning a football game is 0.65. Given that State College has won its football game, the probability of University of State winning its game is over 0.65. The teams are not playing each other. The event State College winning and University of State winning are: a. independent b. mutually exclusive c. dependent

a. independent

The probability that a customer will purchase a product is 0.15. The probability that a customer is male is 0.5. The probability that a customer is a male and will purchase a product is 0.075. The events purchasing a product and being male are. a. independent b. dependent c. mutually exclusive

a. independent

The symbol π in the binomial PDF a. is the probability of success b. is in the interval [0,1] c. is greater than 1 d. can be either negative or positive values

a. is the probability of success and b. is in the interval [0,1]

Which of the following criteria indicate it would be acceptable to approximate the hyper-geometric with a binomial? a. n/N < .05 b. n/N > .05 c. n/N < .10

a. n/N < .05

In which of the following situations is it appropriate to use a Poisson process? [check all that apply] a. The number of people outof 20 who prefer Pepsi-Cola to Coca-Cola in a blind taste test b. The number of customers who purchase concessions every 5 minutes, while a movie is playing at a theater c. Twenty firms are randomly selected from the S&P 500 and asked whether they will increase hiring over the next year. d. The number of landfills per county in the state of Texas.

b. The number of customers who purchase concessions every 5 minutes, while a movie is playing at a theater and d. The number of landfills per county in the state of Texas.

Which of the following should one look for when identifying a hyper-geometric application? [check all the apply] a. sampling with replacement b. a known number of success, s c. a finite population, N d. probability of success is constant

b. a known number of success, s and c. a finite population, N

When calculating a percentile, the first step is to arrange the data set in: a. groups of ten unites b. ascending order (from least to greatest) c. descending order (from greatest to least) d. classes of equal width

b. ascending order (from least to greatest)

The first step to determine the median is to a. fine the average of the data set b. place the data in numerical order c. fine the range of the data set

b. place the data in numerical order

Contingency tables are useful to analyze [check all the apply] a. one quantitative variable b. relative frequencies c. the results of a survey d. one qualitative variable

b. relative frequencies and c. the results of a survey

The range is the difference between a. the first and third quartiles b. the largest and smallest values c. the mean and the median

b. the largest and smallest values

Which of the items describes the usefulness of a standard deviation? a. to compare variables with different unites of measure b. to gauge the relative position of data values within the data set c. to help estimate the mean d. to determine the median of the data set

b. to gauge the relative position of data values within the data set

The probability of randomly selecting a "spade" from a deck of cards is a. 0.33 b. 0.019 c. 0.25 d. 0.077

c. 0.25

Which of the following can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean? a. The mode b. percentiles c. Chebyshev's Theorem d. The empirical rule - assuming a normal distribusion

c. Chebyshev's Theorem and d. The empirical rule - assuming a normal distribusion

Which of the following are examples of conditional probabilities? [check all the apply] a. The probability of Amir purchasing a video game or the probability of Natasha purchasing a video game. b. The probability of Marilyn going to the football game and Tom going to the football game. c. If Neil has already purchased groceries, then the probability of Colleen purchasing groceries. d. The probability of Angel going to the movie, given that Derrick is going to the movie.

c. If Neil has already purchased groceries, then the probability of Colleen purchasing groceries. and d. The probability of Angel going to the movie, given that Derrick is going to the movie.

Choose the logical binomial random variable a. The number of late shipments for two different companies b. The number of late shipments and missing shipments out of the next 12 sent c. The number of late shipments out of the next 12 sent by one company d. The number of late shipments over the next month

c. The number of late shipments out of the next 12 sent by one company

A travel web site wants to provided information comparing hotel costs versus the quality ranking of the hotel for hotels in New York City. One way to summarize this data would be a. a histogram b. a frequency distribution c. a contingency table

c. a contingency table

When comparing two data sets with different unites of measurement, what is the relative measure of dispersion? a. the standard deviation b. the range c. the coefficient of variation

c. the coefficient of variation

The addition rule is used to calculate a. the conditional probability of two events b. The intersection of two events c. the union of of two events d. the independence of two events

c. the union of of two events

When monitoring a process distribution, both the ________ and the ____________ must be tracked.

center, variability

Chebyshev's Theorem says that for any population with mean u and standard deviation o:

k=2 at least 75% will lie within u+/-2o k=3 at least 88.9% will line withing u +/- 3o k=4 at least 93.8% will lie within u +/- 4o

The mean, or average, has the property that distances from the mean to the individual points always sum to:

zero