Econ Stats
The average height for an American male is 71 inches and the standard deviation is 3 inches. What is the z-value for a height of 68 inches?
Z = -1
A random variable can be defined as:
a quantity resulting from a random experiment that can have different values
What are the upper and lower limits of the random variable for the Normal distribution?
No limits. It is asymptotic in both directions.
Which of the following best describes the meaning of "outcome" in the context of a probability experiment?
One and only one result of the experiment.
Which of the following met the requirements for an event?
Toss one coin and the result is a head Roll a die and the result is a 1 Roll a die and the result is a 2, 4 or 6
A fair coin (that is, the probability of "heads" equals 50%) is repeated flipped. What does the Law of Large Numbers predict?
As the number of flips increases, the proportion of "heads" will approach 1/2.
A Uniform Distribution has the same probability for any x such that a≤x≤b. What is this probability?
P(x) = 1/b−a
Which one of the following is a characteristic of the classical approach to probability?
Probabilities assume outcomes of an experiment are equally likely.
Which of the following met the requirements for a probability experiment?
Roll a die Toss one coin Answer a true or false question
What does it mean when an experiment has a set of events that are collectively exhaustive?
That at least one of the events must occur.
Classical probability is based on the assumption:
That the outcomes of an experiment are equally likely.
Which of the following statements best describes permutations?
The order is important Any arrangement of r objects selected from a single group of n possible objects
A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 400 and 500?
0.2139
A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 600 and 700?
0.2706
Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 490 and 560?
0.2823
Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 560 and 640?
0.3133
Applicants for graduate school take a test that has scores which are normally distributed with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen applicant will score between 550 and 650?
0.3851
Applicants for graduate school take a test that has scores which are normally distributed with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen applicant will score between 500 and 600?
0.4186 Reason: z=(500-560)/90=-0.67; z=(600-560)/90=0.44. Use Excel function Normdist or z-tables (0.2486+0.1700).
Suppose that customer usage time of computers in the public library is uniformly distributed with a minimum of 20 minutes and a maximum of 80 minutes. What is the standard deviation of the distribution?
173
The time it takes a wholesaler to fill an order follows a uniform distribution from three to six days What is the probability that they will fill an order between day 3 and 5?
2/3
Which of the following statements best describes a Probability Distribution?
A list of the outcomes of a random experiment and the probability of each outcome.
In a probability experiment, what is an outcome?
A particular result of the experiment.
Choose the statement that best defines the term "experiment" in the context of probability.
A process that leads to only one of several possible outcomes.
P(A or B)=P(A) + P(B) For this to be true, which one of the following conditions must be met?
Event A and event B must not be able to occur at the same time,
Consider the experiment of rolling a die. The event getting a 2 and which one of the following would be considered mutually exclusive?
Getting a 4
Which of the following is a Subjective Probability?
If you apply for a job after graduation, your chance of getting the job is 83%.
How would you describe the shape of the Normal Distribution?
It is "bell" shaped, and symmetrical with the center at μ.
Where does the curve of the normal distribution touch the x-axis?
It never touches, but approaches asymptotically in both directions.
Since the normal probability distribution is symmetrical about the mean, which of the following is true?
The area on each side of the mean is 0.5.
Which is the best definition of the z-value?
The distance between a value x and the mean, μ, divided by the standard deviation, σ
Which one of the following conditions must be met to use the Special Rule of Addition? I.e. P(A or B)=P(A) + P(B)
The events A and B must be mutually exclusive.
What determines the width and location of the Normal Distribution?
The mean (μ) determines the location and the standard deviation (σ) determines the width.
How do you calculate classical probability?
The number of favorable outcomes divided by the number of possible outcomes.
How is Empirical Probability calculated?
The number of times the event occurs divided by the total number of observations.
What is Empirical Probability?
The relative frequency with which the event happened in the past.
Which of the following is an example of a continuous random variable?
The square footage of a house.
Which one of the following is true about events that are both mutually exclusive and collectively exhaustive?
The sum of their probabilities must be 1.
The area under a uniform distribution (or any probability distribution) represents a probability. Which one of the following statements characterizes this area?
The total area is one.
Identical prizes are to be given to two winners from a group of 12 contestants. What counting formula would you use to determine how many ways the prizes could be given out?
combination formula
If the fraction of times an event happened in the past is used as the basis for assigning a probability to the event, this is ______ probability.
empirical
A permutation is any arrangement of r objects selected from n possible objects. Which formula is used to calculate the number of permutations?
nPr = n!/(n−r)!
What shows the possible outcomes of a random experiment and the probability of each outcome?
probability distribution
A quantity representing the outcome of a random experiment that can assume different values is called a:
random variable
Which of the following is the best description of the shape of a uniform distribution?
rectangular
Two events are independent if:
the occurrence of one has no effect on the probability of occurrence of the other
The value given for an Empirical Probability is based on:
the past history of outcomes from the experiment
In a random experiment there are 8 possible outcomes, and two of them correspond to a favorable event. What is the classical probability of the event?
25%
Which of the following is the best definition of "event" in the context of a probability experiment?
a set of one or more outcomes of an experiment
The minimum and maximum values of the random variable are sufficient to describe which of these distributions?
uniform
Which of the following formulas is used to convert a normally distributed random variable, X, to a z-value?
z = (x−μ)/σ
The average weight of a Honeycrisp apple is 110 grams and the standard deviation is 20 grams. What is the z-value for an apple that weighs 140 grams?
z = 1.5
A uniform distribution has a minimum value for the random variable of "a" and a maximum of "b". What is the formula for the mean?
μ = a+b / 2
