STATS CH4&5
the probability of randomly selecting a spade from a deck or cards is
.25 13/52
The prob of Margaret receiving a promotion from XYZ corp is .70. The probability of Katia receiving a promotion ABC inc is .60. If the two promotions are independent then the probability of both Margaret and Katia receiving a promotion is
.42 .70X.60=.42
The probability that a customer purchases popcorn at a theater is .3. What is the probability that the customer doesn't buy the popcorn?
.7 1-.3=.7
Kareem is deciding which college to attend. He believes there is a 55% chance he will attend State and a 33% chance that he will attend Northern Univ. The probability that he will attend either State or northern is.
.88 .55+.33=.88
If two events are mutually exclusive, what is the probability that both occur at the same time
0 (cant occur at the sametime)
The probability of each value x is between
0 and 1
The sum of the probabilities equals
1
Work this 8c5
56
Consists of a series of n independent and identical trials of an experiment such that on each trial there are only two outcomes and each time the trial is repeated
Bernoulli Process
Shows the probabilities associated with the possible values of the binomial random variable.
Binomial probability distribution
Is characterized by (infinitely) uncountable values within any interval
Continuous random variable
Counts the number of successes over a given interval of time or space
Poission random variable
A professor receives, on average, 24.7 e-mails from students the day before the midterm exam. To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution?
Poisson distribution.
What type of probability distribution will most likely be used to analyze the number of chocolate chip parts per cookie in the following problem? The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 6.0. The manager is interested in analyzing the probability that any particular cookie being inspected has fewer than 5.0 chip parts.
Poisson distribution. (b/c it is an interval of time,volume or distance)
This consumer demands a positive expected gain as compensation for taking risk. This compensation increases with the level of risk.
Risk Averse
This consumer completely ignores risk and makes his/her decisions solely on the basis of expected values.
Risk neutral
A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week. Interpret this value.
The expected or average cost for all weekly rat purchases is $13.00.
True or False: When constructing a joint probability table, the cell in the lower right corner must always equal 1.0
True
Which of the following about the binomial distribution is not a true statement?
The random variable of interest is continuous. (it is discrete)
Someone who is risk averse
demands a reward for taking a risk
Assumes a countable number of distinct values. It may assume either a finite number of values or an infinite sequence of values
discrete random variable
a subset of the sample space is an
event
Using the multiplication rule, the probability that event A and event B both occur is computed by multiplying the conditional probability of event A given event B by the probability of
event B
The _______ formula is used to determine the number of possible ways to arrange n items when there are no groups.
factorial (Factorial is applied when there are no groups)
The ______ formula is used to determine the number of ways to arrange x objects from a group of n objects where the order of the objects matters.
permutation
the expected value of a distribution is also referred to as the
population mean
A probability based on logical analysis rather than observation or personal judgement is best referred to as a
priori probability
Is a numerical value that measures the likelihood that an uncertain event occurs. This value is between 0 and 1 where a value of one indicates definite events.
probability
a numerical value that measures the likelihood of an uncertain event is a
probability
This variable summarizes outcomes of an experiment with numerical values,
random
What are two examples of mutually exclusive events
recieving an A and recieving a b plus as a final grade in an accounting class being on time and being late for an appointment
When calculating the probability of x successes in n trials of a binomial experiment, the probability of success and the probability of failure
remain the same, even when a probability is calculated for a different value of x
All possible outcomes of an experiment is the _____ space.
sample
A probability based o personal judgement rather than on observation or logical analysis
subjective
A softball coach believes that laurie has a .5 prob of getting a hit against a certain pitcher. This type of probability is best characterized as a
subjective probability
If X is a Poisson random variable, then
the mean is equal to the variance
If two events are independent then the probability that both events occur equals
the multiplication of the individual probabilities
What is an example of a Poisson random variable
the number of leaks in a specified stretch of pipeline the number of customers who purchase concessions over the next hour at a theater
In a binomial distribution
the probability of success p is stable from trial to trial.
What is not an example of an experiment
the winner of last week's lottery drawing
Contingency tables are useful to analyze
two categorical variables
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 order of the objects is irrelevant
combination
for any given event the probability of that event and the probability of the ______ of the event must sum to one.
complement
For hotels in NYC a travel web site wants to provide info comparing hotel costs versus the quality ranking of the hotel. A useful way to summarize this data is to construct a
contingency table
A discrete uniform distribution has what 3 characteristics
-the distribution has a finite number of values - each value is equally likely -the distribution is symmetric
A random experiment satisfies a poisson process if
-the number of successes with in a specified time or space interval equals and integer between 0 and infinity -the number of successes counted in non overlapping intervals are independent -the probability that success occurs in any interval is the same for all intervals of equal size
The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be exactly 3 power outages in a year is ____________.
.09 mean= 6 x= 3 (mean^x)(e^-mean)/x! (6^3)(e^-6)/3! = .089=.09
An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is the probability that precisely half of the members will be women?
.12 How: 18-m 6-w 6-members ( 18c3 )X( 6c3 ) (816) X (20) = 16,320 18+6=24 24c6= 134,596 16,320/134,596=.121
The number of customers that use the atm averages 2.3 over a 30 minute interval. If the use of the atm machine is Poisson distributed, then the probability that exactly one customer uses the atm machine in a 30 minute interval is
.23 how: (e^-2.3)(2.3^1)/1!=2.3
From long experience, NoFlat Tire knows that the probability is .55 that their XB-70 will last 80,000 miles before it becomes bald or fails. An adjustment is made on any tire that does not last 80,000 miles. You purchase four XB-70s. What is the probability only 3 tires will last at least 80,000 miles?
.3 How: x=4 n=3 p=.55 4c3 X (.55^3)(1-.55)^4-3 4X(.166375)(.45) 4X(.07486875) =.299=.3
The highroller casino puts the odds of a certain baseball team winning the world series at 1 to 30. Based on those odds what is the probability that they actually win
0.032 1/1+30 = 0.032
A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet, what is the probability that all 4 students selected are undergraduate students?
0.0625
The sum of the probabilities of a list of mutually exclusive and exhaustive events is
1
If two events are collectively exhaustive, what is the probability that one or the other occurs.
1.00 (takes up the entire sample space)
binomial distribution describes the behavior of a count variable X if the following conditions apply:
1: The number of observations n is fixed. 2: Each observation is independent. 3: Each observation represents one of two outcomes ("success" or "failure"). 4: The probability of "success" p is the same for each outcome.
The probability that a customer will purchase a product is .15. The probability that a customer is a male is .05. The probability that a customer is male and will buy the product is .075. The events purchasing a product and being a male are
Independent (Since there is a probability that both events can occur)
What type of probability distribution will most likely be used to analyze the number of chocolate chip parts per cookie in the following problem? The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 6.0. The manager is interested in analyzing the probability that any particular cookie being inspected has fewer than 5.0 chip parts.
Poisson
On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery store. What type of probability distribution can be used to find out the probability that there will be no customer arriving at a checkout counter?
Poisson distribution
What are 2 examples of discrete random variables
The number of students who received and A on their sats exam The number of people who vote for the democratic candidate in the next presidential election
What is an example of a conditional probability
The probability that Lisa purchases groceries, given that Neil has already bought groceries
The expected value of the discrete random variable X is
a weighted average of all possible values of X
A probability distribution is an equation that
associates a particular probability of occurrence with each outcome in the sample space.
What are 2 examples of a binomial experiment
Asking customers at a movie theater if they spent $20 or more at concessions Asking randomly selected people whether they are a member of Facebook
What is a good example of an empirical probability
Based on past data, a manager believes that there is a 70% chance of retaining an employee for at-least a year
