exam 2
which of the following represents an empirical probability? -the prob of tossing a head on a coin is 0.5 -based on past observation, a manager believes there is a 3 in 5 chance of retaining employee -a skier believes she has a 0.10 chance at winning gold -the prob of rolling a 2 on a single die is 1 in 6
-based on past observation, a manager believes there is a 3 in 5 chance of retaining employee
If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.5, then P(A ∩ B) = 0.20 0.00 0.90 0.10
0.00
If a coin is tossed three times, the likelihood of obtaining three heads in a row is 0.875 0.125 0.500 zero
0.125
For a standard normal distribution, the probability of z ≤ 0 is -0.5 0.5 one zero
0.5
The occurrence of the event isjust as likely asit is unlikely
0.5
If a penny is tossed four times and comes up heads all three times, the probability of heads on the fourth trial is larger than the probability of tails 0.0625 zero 0.5000
0.5000
In a standard normal distribution the probability of z being less than or equal zero is much larger than 1 0.5000 0.0000 there is no answer to this question, since the value of the mean is not known
0.5000
what are the two key properties of a discrete probability distribution? -1<P(X=x)<1 and sigmaP(X=xi)=0 0<P(X=x)<1 and sigmaP(X=xi)=0 0<P(X=x)<1 and sigmaP(X=xi)=1 -1<P(X=x)<1 and sigmaP(X=xi)=1
0<P(X=x)<1 and sigmaP(X=xi)=1
If a dime is tossed four times and comes up tails all four times, the probability of heads on the fifth trial is smaller than the probability of tails larger than the probability of tails 1/2 1/32
1/2
If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is 1/2 larger than the probability of tails 1/16 zero
1/2
If a six sided die is tossed two times, the probability of obtaining two "4s" in a row is 1/96 1/36 1/216 1/6
1/36
The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old? 1.96% 50% It could be any value, depending on the magnitude of the standard deviation 21%
50%
Which of the following statements is always true? P(A) = 1 - P(Ac) -1 ≤ P(Ei) ≤ 1 ∑P ≥ 1 P(A) + P(B) = 1
P(A) = 1 - P(Ac)
A ______ distributed random variable is often useful in estimating the number of occurrences over a specified interval of time or space.
Poisson
Two Properties of a ______ Experiment 1. The probability of an occurrence is the same for any two intervals of equal length. 2. The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval.
Poisson
In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the normal distribution Poisson distribution binomial distribution uniform distribution
Poisson distribution
is a numerical measure of the likelihood that an event will occur
Probability
Which of the following is correct? a discrete random variable has a probability mass function but no a cumulative distribution function a continuous random variable has a probability density function, and a discrete random variable has a probability mass function a continuous random variable has a probability mass function, and a discrete random variable has a probability density function a continuous random variable has a probability density function but not a cumulative distribution function
a continuous random variable has a probability density function, and a discrete random variable has a probability mass function
In statistical experiments, each time the experiment is repeated a different outcome may occur a different out come must occur the same outcome can not occur again the same outcome must occur
a different outcome may occur
Variance is a measure of the dispersion of a random variable the sum of the squared deviation of data elements from the mean a measure of the average, or central value of a random variable the square root of the standard deviation
a measure of the dispersion of a random variable
A graphical method of representing the sample points of an experiment is a tree diagram an ogive a histogram a frequency polygon
a tree diagram
When a continuous probability distribution is used to approximate a discrete probability distribution a value of 0.5 is added and/or subtracted from the area a value of 0.5 is added and/or subtracted from the value of x a value of 0.5 is subtracted from the area a value of 0.5 is added to the area
a value of 0.5 is added and/or subtracted from the value of x
Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is true about the z value corresponding to a given x value? A positive z=(x-avg)/st dev indicates how many st devs x is above avg A negative z=(x-avg)/st dev indicates how many st devs x is below avg the z value corresponding to x=avg is zero all of the above
all of the above
A probability near one indicates
an event is almost certain to occur
A probability near zero indicates
an event is quite unlikely to occur
If P(A) = 0.25, P(A│Y) = 0.35, and P(A│X) = 0.10, then events A and Y could be either independent or dependent, depending on the value of Y are dependent could be either independent or dependent, depending on the value of X are independent
are dependent
Four Properties of a _______ Experiment 1. The experiment consists of a sequence of n identical trials. 2. Two outcomes, success and failure, are possible on each trial. 3. The probability of a success, denoted by p, does not change from trial to trial. (This is referred to as the stationarity assumption.) 4. The trials are independent.
binomial
In a standard normal distribution the value of z cannot be negative cannot be larger than 3.09 cannot be larger than 0.50 can be any value
can be any value
Assigning probabilities based on the assumption of equally likely outcomes
classical method
When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the relative frequency method subjective method probability method classical method
classical method
A value of 0.5 that is added and/or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called 50% of the area under the normal curve continuity correction factor factor of conversion
continuity correction factor
A _______ random variable may assume any numerical value in an interval or collection of intervals.
continuous
A _________ random variable may assume either a finite number of values or an infinite sequence of values.
discrete
The _______ ______, or mean, of a random variable is a measure of its central location.
expected value [E(x)]
The required conditions for a discrete probability function are: _________ and _______
f(x)>0 and ∑f(x)=1
If the probability of event A is not changed by the existence of event B, we would say that events A and B are __________.
independent
The _____ of events A and B is the set of all sample points that are in both A and B
intersection P(A ∩ B)
The standard deviation of a standard normal distribution is always equal to zero is always equal to one can be any positive value can be any value
is always equal to one
a continuous random variable has the uniform distribution on the interval [a,b] if its probability density function f(x) __________. -is constant for all x between a and b, and 0 otherwise -asymptotically approaches the x axis to infinity or decreases to negative infinity -is bell-shaped between a and b -is symmetric around its mean
is constant for all x between a and b, and 0 otherwise
The probability that a continuous random variable takes any specific value is very close to 1.0 depends on the probability density function is equal to zero is at least 0.5
is equal to zero
In a standard normal distribution, the range of values of z is from -3.09 to 3.09 -1 to 1 0 to 1 minus infinity to infinity
minus infinity to infinity
The intersection of two mutually exclusive events can be any positive value can be any value between 0 to 1 must always be equal to 1 must always be equal to 0
must always be equal to 0
Two events are said to be ________ if the events have no sample points in common.
mutually exclusive
A description of the distribution of the values of a random variable and their associated probabilities is called a probability distribution expected value random variable random variance
probability distribution
The ______ ______ for a random variable describes how probabilities are distributed over the values of the random variable.
probability distribution
Assigning probabilities based on experimentation or historical data
relative frequency method
The variance is a measure of dispersion or variability of a random variable. It is a weighted average of the square root of the deviations from the mean squared deviations from the median squared deviations from the mean square root of the deviations from the median
squared deviations from the mean
Assigning probabilities based on judgment
subjective method
Which of the following can be represented by a continuous random variable? the number of typos found on a randomly selected page the number of customer who visit a store on friday the average temperature in tampa, fl in july the number of students who will get financial aid at msu
the average temperature in tampa, fl in july
what can be said about the expected value and st dev of an exponential distribution? -the expected value is equal to the square root of the st dev -the expected value is equal to the square of the st dev -the expected value is equal to the st dev -the expected value is equal to the reciprocal of the st dev
the expected value is equal to the st dev
which of the following does not represent a continuous random variable? height of oak trees in park time of flight between chicago and new york the number of customer arrivals to a bank between 10am and 11am heights and weights of newborn babies
the number of customer arrivals to a bank between 10am and 11am
In a binomial experiment the probability does not change from trial to trial the probability does change from trial to trial None of these alternatives is correct. the probability could change from trial to trial, depending on the situation under consideration
the probability does not change from trial to trial
The set of all possible outcomes of an experiment is the population the sample space an experiment an event
the sample space
What does it mean when we say that the tails of the normal curve are asymptotic to the x axis? the tails get closer and closer to the x axis and eventually cross this axis the tails get closer and closer to the x axis and eventually become this axis the tails get closer and closer to the x axis but never touch it the tails get closer and closer to the x axis and eventually touch it
the tails get closer and closer to the x axis but never touch it
Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable? exactly two outcomes are possible on each trial the probabilities of the outcomes do not change from one trial to another the trials are dependent the experiment has a sequence of n identical trials
the trials are dependent
The _____ of events A and B is the event containing all sample points that are in A or B or both
union P(A U B)
summarizes the variability in the values of a random variable
variance (o^2)
If two events are mutually exclusive, then their intersection [P(A ∩ B)] must be larger than zero, but less than one will be equal to zero will be one can have any value larger than zero
will be equal to zero
for an experiment in which a single die is rolled, the sample space is {1,1,3,4,5,6} {1,2,3,4,4,5} {2,1,3,6,5,4} all of the above
{2,1,3,6,5,4} -lists all possible outcomes
which of the following is not an event when considering the sample space of tossing two coins? {HH, TT, HTH} {HH, HT, TH, TT} {HH, TH} {HH, TH, HT}
{HH, TT, HTH} (bc HTH would be tossing three coins)
the intersection of events A={apple, peach, pumpkin} and B={cherry, blueberry, pumpkin} is? {apple, peach, pumpkin, cherry, blueberry} {pumpkin} {apple, peach, cherry, blueberry} {apple, peach, cherry, blueberry, pumpkin}
{pumpkin}
Which of the following is a required condition for a discrete probability function? ∑f(x) = 1 for all values of x f(x) 1 for all values of x ∑f(x) = 0 for all values of x f(x) < 0 for all values of x
∑f(x) = 1 for all values of x