CBAD - Statistics 2
Chapter 6: The following table represents the number of cartons of milk that the children at Hoover-Wood Element school purchase for lunch.
.08 1.0-0.2-07-0.02
Chapter 5: Calculate the marginal probability that a country club member does not play golf
.25 100/400 = .25
Chapter 5: A subset of the sample space is a/an
Event
Chapter 5: Classical approach
use deduction to determine P(A)
Chapter 6: 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?
1 - P(X<_ 3)
Chapter 5: 82% of companies ship their products by truck. 47% of companies ship their product by rail. 40% of companies shipped by truck and rail. What is the probability that a company ships by truck or rail?
0.89
Chapter 5: The following contingency table was created by a marketing firm to show which customers were considered younger and which were considered older as well as showing if they were monthly, weekly shoppers
90
Chapter 5: The following contingency table was created by a middle school to determine the relationship between a student taking a foreign language (either Spanish or French) and whether the student plays in the school band
90
Chapter 5: Marginal
P(S3) = 17/67 = .2537
Chapter 6: The symbol pie in the binomial PDF
is the probability of success, is in the interval [0,1]
Chapter 5: The probability of State College winning a football game is.6. The probability of University of State winning a football game is 65. Given that State College has won its football game, the probability of University of State winning its game is .65The teams are not playing each other The events State College winning and University of State winning are
independent
77777 It is meaningful to compute the probability that a continuous random variable
is between two numbers, is less than or equal to the number, is greater than or equal to a number
Tthe triangular distribution
is bounded by the interval [a,c], is useful for what if analysis
77777 A random variable is said to be continuous if it
is measured over an interval, can have decimal values
Chapter 5: Probability
likelihood that a particular event will occur
7777 The standard deviation of the standard normal distribution is
one
A Poisson process is used to observe the number of occurrences
overtime or in space
Chapter 5: Subjective approach
probability is needed when there's no repeatable random experiment for example what is the probability that Fords new supplier of plastic fasteners will be able to meet the September 23 shipment deadline or what is the probability that a new truck product program will show a return on investment of at least 10%, or what is the probability that the price of Forte stock will raise within the next 30 days
Chapter 5: Subjective
probability reflects someone's informed judgment about the likelihood of an event
Chapter 5: The set of all possible outcomes from a random experiment is called a
sample space
Chapter 5: 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 the intersection P(A∪B)=P(A)+P(B)−P(A∩B)
Chapter 6: Which of the following experiments is likely to produce a uniform discrete distribution?
the values that occur from repeated spins of a roulette wheel at a casino the answer selected on a multiple choice question that has four choices by a student who did not study
Chapter 5: Bayes' _________ is used to revise probabilities when one has new ______\\
theorem, information
Chapter 6: In which of the following ways are binomial distributions and hypergeometric distributions similar?
they are both discrete distributions, they have two possible outcomes success or failure
Chapter 5: Intersection
two events A and B is the event consisting of all outcomes in the sample space S that are contained in both event A and event B
Chapter 5: prior probability for event A is the _______ probability whereas the prosterior probability event A is the __________ probability
unconditional conditional
Random variables are represented by___case letters while particular values of random variables are represented by___case letters
upper, lower
an example of a random variable that closely followed the normal distribution is
weight of a box of cookies
An example of random variable that closely follows the normal is
weights of newborn babies
Chapter 5: Complement
P(A) + p(A') = 1
If the continuous uniform random variable, Xassumes the values a and bas its lower and upper a + b limits respectively, then represents the of
mean
Chapter 6: Which of the following criteria indicate it would be acceptable to approximate the hypergeometric with the binomial?
n/N < .05
When a random process counts the number of arrivals over a random time interval we are also interested in the _______ between two arrivals.
time
True or false: Under appropriate circumstances, many discrete random variables can be described by the normal distribution.
true
to find the P(Z>0.93) find the row containing ______ in the far left column. Then find the column containing _____ in the top row. P(Z>0.93) = 1 - _________ (round to 4 decimals) = ______ (round to four decimal)...(Please use Appendix C-2.)
0.8, 0.03, 0.8238, 0.1762
Chapter 6: The average number of customers arriving at Jimmy's Burgers is 17 per minute . What is the probability only 1 customer arrives in the next minute?(Round to three decimals and do not enter a percentage)
1.7^1e^-1.7 / 1! = .311
Chapter 6: The average number of customers arriving at Jimmy's Burgers is 17 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.)
1.7^1e^-1.7 / 1! =.311
XYZ corporation makes widgets. 1% of the widgets are defective. XYZ manufactures 100,000 widgets, the number of defective widgets is expected to be
1000 100,000 x 0.01
A random variable X has... 25....5.....5x... Y = ?
125
Chapter 6: 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.
230x0.2 = 46
Chapter 6: 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
Chapter 6: In which of the following situations is it appropriate to use a Poisson process?
The number of customers who purchase concessions every five minutes, while a movie is playing at a theater The number of landfills per county in the state of Texas
the formula to calculate probability for the hypergeometric distribution, what does the denominator represent?
The number of ways a sample size n can be selected from the population of size N
Chapter 5: Which of the following are examples of conditional probabilities?
The probability of aunt Joe going to the movie, given that Derek is going to the movie. if Neil has already purchased groceries, then the probability of cam purchasing groceries.
Chapter 5: Union
Two events consist of all outcomes in the sample space capital S that are contained either an event A or an event B or in both
7777 It is appropriate to approximate the Poisson distribution with the normal distribution when
Y (upside down) is large
Chapter 5: events are considered ___________ ___________ if the union of these events is The entire sample space
collectively exhaustive
Chapter 5: The tree diagram has how many probabilities at the terminal end of each branch
conditional
Chapter 5: Using the multiplication rule, the joint probability of event A and event B is computed by multiplying the conditional probability of event A given event B by the probability of
event B
Chapter 5: True or false: The General Law of Multiplication is used to calculate the probability of the union of two events
false
Chapter 6: A binomial distribution is skewed left when the probability of success is
greater than .5
Chapter 5: calculate the marginal probability that a country club member plays tennis and golf
.45
The z score associated with the highest 10% is closest to
1.28
Chapter 5: P(A)=0
Event cannot occur
Chapter 5: Playing tennis and playing golf are ____________ (choose between dependent and independent)
dependent
Chapter 5: to calculate a union for two mutually exclusive events,
simply add the individual probabilities of the two events
The expected value of the sum of two or more random equal to the _______ their individual expected values
sum
7777 The probability that a continuous random variable takes on a particular value is zero because of which of the following reasons?
The area under a curve capital AT a certain point is zero
Chapter 5: A conditional probability is calculated by dividing the probability of the intersection of two events by the probability of...
The given event
To calculate the variance of the sum of two independent random variables
The individual variances are summed
7777 Binomial probabilities can be difficult to calculate, and therefore appropriate to approximate,
n is large
77777 The z score associated with the lowest 2.5% of a normal distribution will be
negative
77777 Which of the following is an example of a continuous random variable?
normal
Chapter 5: If 180 of the 400 country club members play tennis and golf, 180 would be placed in the contingency table in the cell with the letter
A
Chapter 5: Events that cannot both occur at the same time are mutually ________ events
Exclusive
Chapter 5: Which theorem provides a method for revising probabilities to reflect new information ?
BAYES THEOREM
Chapter 6: choose the logical binomial random variable
The number of late shipments out of the next 12 sent by one company
77777 True or false continuous rondom can have a finite set of Integer values,
false
Chapter 5: Suppose in a population of adults there are 10% that are avid fly fishermen/womenIf we were to choose a random sample of 10 adults from this population the law of large numbers says
that the percent of fishermen/women in this sample might not equal 10% but as the sample gets farger the percent will get closer to 10%.
Chapter 6: In which of the following situations is it appropriate to use a Poisson process?
the number of calls arriving to a customer help line in a one hour period
Chapter 5: Sample space
the set of all possible outcomes
77777 What is the use of the cumulative distribution function, F(x) of a continuous random variable?
to find the probability that X is less than or equal to any value X
Chapter 5: Do you calculate a joint probability from a contingency table, the frequency of each cell is divided by the...
total number of outcomes in the sample space
Chapter 5: True or false: probability is a number that describes uncertainty
True
Chapter 6: In the binomial distribution which expression represents the probability of failure?
1-PIE SYMBOL
Chapter 5: 5!=?
120
Chapter 5: A country club has 50 members out of a total of 400 members who play neither tennis nor golf. The value 50 should be inserted into the contingency table in the cell with the letter
C. This cell includes non-tennis players, but it includes golfers and non-golfers.
Chapter 5: Three views of probability and their meaning
Empirical; estimated from observed outcome frequency, example there's a 3.2% chance of twins in a randomly chosen birth classical; known a prioriti by the nature of the experiment, example there is a 50% chance of heads on a coin flip subjective; based on informed opinion or judgment, example there is a 60% chance that Toronto will bid for the 2024 winter Olympics
Chapter 5: Random experiment
Observational process whose results cannot be known in advance
Chapter 5: Probability of the complement of a is found by subtracting the probability of A from 1
P(A') = 1-P(A)
Chapter 5: If events A and B are independent, then
P(A∩B)=P(A)P(B)
Chapter 5: If A and B are mutually exclusive events, then P(A ∩ B) = 0 and the general addition law can be simplified to the sum of the individual probabilities for A and B, the special law of addition.
P(A∪B)=P(A)+P(B)(addition law for mutually exclusive events) For example, if we look at a person's age, then P(under 21) = .28 and P(over 65) = .12, so P(under 21 or over 65) = .28 + .12 = .40 because these events do not overlap.
Chapter 6: Which of the following should one look for when identifying a hypergeometric application?
a known number of success, s a finite population, N
A triangular distribution that has a mode = 0 and has a lower 1imit = - 2.45 and an upper limit 2.45 is similar to
a standard normal
Chapter 6: Which of the following is an example of a binomial experiment
asking randomly selected people if they are a member of Facebook, ask customers at a movie theater if they spent $20 or more on concessions
777777 The probability that a discrete random variable equals any of its values is
between zero and one, inclusive
7777 Which of the following is an example of a discrete random variable?
binomial
True or false: A Bernoulli experiment has three possible outcomes.
false
Chapter 5: if two events are independent, then the joint probability of the two events is calculated by...
multiplying the probability of the two events
variance represents the O^2
true
Chapter 6: An apartment complex rents an average of 2.3 new units per week. If the number of apartments rented each week is Poisson distributed, then the probability of renting no more than 1 apartment in a week is
(e^-2.3)(2.3^1) / 1! + (e-2.3)(2.3^0) / 0!
Chapter 6: An apartment complex rents an average of 2.3 new units per week. If the number of apartments rented each week has a Polsson distribution, then the probability of renting exactly three apartments in a week is
(e^-2.3)(2.3^3) / 3! = 0.203
Chapter 5: Calculate the conditional probability that a country club member does not play tennis given that they do not play golf
.5
Chapter 5: calculate the marginal probability that a country club member plays tennis
.575 230/400=.575
7777 A normal random variable X has a mean = 100 and a standard deviation n = 20 P(X <= 110) = Round your answer to 4 decimals.
.6915
Chapter 5: Corey and Laurie process purchase orders for Acme Inc. Laurie processes 60% of the purchase orders, Cory process is 40% of the purchase orders. 5% of lorries purchase orders have errors and 2.5% of Coreys purchase orders have errors. A purchase order has an error; the probability that Laurie processed the erroneous purchase order is... Round your answer to two decimal places
.75
Chapter 5: Calculate the conditional probability that a country club member plays golf given that they play tennis
.783
A list of the top twenty restaurants in Chicago was released. Four of the restaurants specialize in seafood. If five of the restaurants are selected randomly from the list, the standard deviation for the number of restaurants specializing in seafood is 7947(round your answer to 4 decimal places).
.7947
Chapter 6: A company receives an average of .64 purchase orders per minute. Assuming a Poisson distribution for the number of purchase orders per minute, what is the standard deviation for this distribution?
.8
Chapter 5: In order to make sure Sam gets to his final exam on time he said three alarm clocks that work independently of each other. Assume the probability of any one of the alarm clocks working is equal to .98. What is the probability that Sam is late to his final exam?
0.000008 P(late) = P(all three alarms fail) = .02x.02x.02
Chapter 5: XYZ Corp. has filled 100,000 purchase orders during its existence. 1,100 of the purchase orders have had errors. Using an empirical probability, the probability of the next purchase order having an error is __________ (round your answer to three decimal places and enter as a probability not a percentage)
0.011
Chapter 5: The sports book at the highroller Casino put the odds of a certain baseball team to win the World Series at one; 25 (1 to 25). Based on those odds, what is the probability that this baseball team will win the World Series?
0.0385 1 / (1+25) equal to 0.0385
Chapter 5: The phone relative frequencies help determine if a residence location affects whether the residents get season passes to the pool located on the west side. What is the probability that a resident lives on the west side and does not have a season pass?
0.1
Chapter 6: Professor Stats has 40 students in her statistics class. 24 of the students are male. If she randomly selects 6 of her students at random, without replacement, the probability of selecting 4 men in the sample is
0.332
Chapter 5: The probability of a customer purchasing popcorn at the movie theater is 0.3. What is the probability that a customer will not purchase popcorn?
0.7
Chapter 5: The probability of Anthony being on time for work is 0.9. The probability that Anthony will take the train to work is 0.8. The probability that Anthony will be on time for work if he took the train is 0.95. The probability that Anthony is on time for work and took the train is... round 2 decimal places
0.76 0.95 x 0.8 = 0.76
A list of the top twenty restaurants in Chicago was released. Four of the restaurants specialize in seafood. five of the restaurants are selected randomly from the listthe expected value for the number of restaurants specializing in seafood is
1
Chapter 5: The highest possible probability, of the choices below, for an event is
1.0
The median of an exponential distribution with lambda = 0.3 arrivals per minute is
2.3
Chapter 5: Mike is placing a bet on an upcoming horse race in which seven 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 how many possible outcomes for the first three horses in the correct order.?
210
Chapter 6: 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 the company use for the mean to help alculate the probability?
4
For a continuous random variable X with a = 10 and b = 20, P(X <= 14) =
4
Chapter 6: 20% of a restaurant's customers order the chef's special. customers are anticipated to dine tonight at the restaurant. The expected number of chef's specials that will be ordered tonight is
46 (230x0.2=46
Chapter 6: Generally, a hypergeometric distribution will be used instead of a binomial distribution when
Independence of the trials is uncertain, there is a finite population, sampling is done without replacement
Chapter 5: The __________ (one word) Of two events A and B contains only those outcomes that are in both A and B
Intersection
7777 Which Excel expression would be used to find the X value associated with the highest 10% if has a mean = 100 and a standard eviation = 20
NORM.INV(.99,100,20)
7777 Which probability statement below represents a cumulative probability
P(Z<_-2.34)
7777 Which of the following statements about the variance of a continuous random variable are true?
The standard deviation is the square root of the variance, the variance is the weighted average of the squared deviations from the mean
A ____ random variable is the sum of repeated Bernoulli trials
binomial
Chapter 6: The binomial distribution can be approximated using the Poisson
by letting ʎ = nπ when n is large and π is less than or equal to .05
Chapter 5: If 230 out of 400 country club members play tennis, we would place 230 in the following contingency table in the cell with the letter
c
Chapter 5: A probability that can be deducted through logical reasoning before an experiment is performed is what type of probability?
classical
Chapter 6: Which of the following are characteristics of a discrete uniform distribution?
distribution is symmetric, the probability of each value of the random variable is the same, the random variable has a finite number of outcomes
For each trial the probability of success remains the same
each trial has only two possible outcomes, each trial is independent of the previous trial, for each trial the probability of success remains the same
77777 One characteristic of a well-defined probability density function of a continuous random variable X is that the area under the curve, f(x) over all values of x is
equal to one
Chapter 5: P(A)=1
event is certain to occur
The normal distribution is the most extensively used distribution in statistical studies because
it has important features used in sampling and estimation, economic and financial data often displayed bell shaped distribution's, many physical measurements have a bell shaped distribution
Chapter 5: The multiplication rule is used to calculate what type of probability
joint
Chapter 5: An important theorem in probability states that as the number of trials increase, an empirical probability approach the theoretical probability. This theorem is called the ___________ of _______ _______
law of large numbers
Chapter 5: Dimitri is the coach of the high school mathleets team. There are 8 mathleets but only five may represent the school of the upcoming math tournament. How many ways can dimitri randomly choose 5 mathleets from the 8 eligible math leets?
56
If the mean time between arrivals 10 minutes then the average arrival rate is
6 hour
Chapter 6: 20% of restaurants customers order chefs special. 230 customers are anticipated to at the restaurant tonight. The standard deviation for this binomial distribution is your answer to 3 decimal places
6.066
Chapter 5: Graduates with the top three highest GPAs will be honored as the school's graduation ceremony. The highest GPA will receive the Gold Award, the second highest will received the Silver Award, and the third highest GPA will receive the Bronze Award. If there are 10 graduating seniors, how many different arrangements of honored students are possible?
720 10!(10-3)!
Chapter 6: Which of the following are characteristics of the geometric distribution ?
A Series of Bernoulli trials, counts the number of trials until the first success
Chapter 5: which statement given below is correct
A and B are dependent events because P(B | A) ≠ P(B) or 35/60 ≠ 85/120 A and B are dependent events because P(A | B) ≠ P(A) or 35/85 ≠ 60/120
Chapter 5: A travel website wants to provide 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 contingency table
Consider a random variable X that denotes a random delivery time anywhere between 9 am and 10 am . X would reasonably be
A continuous uniform random variable
Chapter 6: Generally, a positive covariance between assets^ prime ' returns in a portfolio indicates
A greater risk in investing in the portfolio
Chapter 5: for any given event, the sum of probability of that event and the probability of its _________ Must equal one
Complement
Chapter 5: True or false: The probability of winning a lottery is .0000000012. The Law of Large Numbers says that because this probability is so small, no one should ever win a lottery.
False
Chapter 5: The people who are involved in which of the following areas talk more commonly about odds rather than speaking of probability
Games of chance, sports
Chapter 5: Conditional
P(S3 | T1) = 1/16 = .0625
Chapter 5: The following contingency table can help determine if a residence location is independent of whether or not the resident purchases a season pass to the pool. The pool is located on the west side. For which comparison of the probabilities would you choose to show dependent switching a residence location and whether or not they purchased a season pass
P, season pass and lives west. P, seasons pass P, seasons pass and lives east. P, seasons pass
A variable that assigns numerical values to the outcomes of a random experiment
Random
Chapter 5: A trial, or process, that produces several possible outcomes that cannot be known in advance is called an/a ......
Random experiment
Chapter 6: 20% of a restaurants customers order the chef's special230 customers are anticipated to dine at the restaurant tonight. The standard deviation for this binomial distribution is (round your answer to 3 decimal places).
SQUARE ROOT... 230x0.2x0.8 = 6.066
Chapter 5: A probability is signed by a person that is based on that person's judgment or experiences is a _______ Probability
Subjective
Chapter 5: Event
Subset of outcomes in the sample space
Chapter 5: Simple event
an elementary event, a single outcome
Chapter 6: Discrete random variables
are countable, can have finite or infinite number of values, have a set of distinct values
Chapter 5: define event A = {1, 2, 3, 4} and event B = {2, 3, 6, 7}. AuB =
{1,2,3,4,6,7}
