Test 3
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)--10 outcomes
State the criteria for the binomial criteria experiment..
-trial independent -probability of success p remains constant -Each trial has two possible mutually exclusive outcomes: success and failure. -The experiment consists of a fixed number, n, of trials. ***all the above
Suppose you toss a coin 100 times and get 58 heads and 42 tails. Based on these results, what is the probability that the next flip results in a tail?
.42
43.1% of 3-year-olds are enrolled in day care. What is the probability that a randomly selected 3-year-old is enrolled in day care?
.431
In a recent survey, it was found that the median income of families in country A was $ was $57,400. What is the probability that a randomly selected family has an income greater than $57 comma 400?
.50
What is the probability of an event that is impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is impossible?
0; NO
What are the two requirements for a discrete probability distribution?
0<( or equal to)P(x)<(or equal to) 1 ETHE SUM of P(x)=1
The area under the normal curve to the right of mu equals _______.
1/2
Suppose Aaron is going to build a playlist that contains 5 songs. In how many ways can Aaron arrange the 5 songs on the playlist?
5nPr5=120
What is a discrete probability distribution?
A discrete probability distribution lists each possible value a random variable can assume, together with its probability.
What is a random variable?
A random variable is a numerical measure of the outcome of a probability experiment.
Describe what an unusual event is. Should the same cutoff always be used to identify unusual events? Why or why not?
An event is unusual if it has a low probability of occurring. The same cutoff should not always be used to identify unusual events. Selecting a cutoff is subjective and should take into account the consequences of incorrectly identifying an event as unusual.
Describe how the value of n affects the shape of the binomial probability histogram.
As n increases, the binomial distribution becomes more bell shaped.
Explain the Law of Large Numbers. How does this law apply to gambling casinos?
As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome. This applies to casinos because they are able to make a profit in the long run because they have a small statistical advantage in each game.
What happens as the value of n increases and the probability of success remains the same?
Becomes more symmetric/ bell-shaped
is an arrangement of r objects chosen from n distinct objects without repetition and without regard to order.
Combination; order does NOT matter
Home attendance for a game of football Annual traffic fatalities in a country.
Discrete because it'a random variable that is countable.
What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p?
E(x)=np
In probability, a(n) ________ is any process that can be repeated in which the results are uncertain.
Experiment
For it to be unusual
Has to be less than .05
Two events E and F are ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.
Independent
The word AND in probability implies that we use the ________ rule. OR If two events are disjoint, then they are independent
Multiplication Addition FALSE
A hockey player who makes 21% of his shots is asked to make his shots until he misses. The number of shots attempted is recorded Binomial Experiment?
No because the experiment is not performed a fix number of times.
If events E and F are disjoint and the events F and G are disjoint, must the events E and G necessarily be disjoint? Give an example to illustrate your opinion
No, events E and G are not necessarily disjoint. For example, E={0,1,2}, F={3,4,5}, and G={2,6,7} show that E and F are disjoint events, F and G are disjoint events, and E and G are events that are not disjoint.
If E and F are disjoint events ,then P(E or F)= If they ARE NOT disjoint events, then
P(E)+P(F) P(E)+P(F)-P(E and F)
is an ordered arrangement of r objects chosen from n distinct objects without repetition.
Permutation
Describe the difference between classical and empirical probability.
The empirical method obtains an approximate empirical probability of an event by conducting a probability experiment. The classical method of computing probabilities does not require that a probability experiment actually be performed. Rather, it relies on counting techniques, and requires equally likely outcomes.
A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.
The histogram is bell shaped so normal distribution could be used.
In a certain card game, the probability that a player is dealt a particular hand is 0.32. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly 32 times? Why or why not?
The probability 0.32 means that approximately 32 out of every 100 dealt hands will be that particular hand. No, you will not be dealt this hand exactly 32 times since the probability refers to what is expected in the long-term, not short-term.
What are the two conditions that determine a probability distribution?
The probability of each value of the discrete random variable is between 0 and 1, inclusive, and the sum of all the probabilities is 1.
The number of points scored in a basketball game. The weight of steak.
The random variable is discrete. The possible values are x= 0,1,2,3 The random variable is continuous. The possible values are
The normal curve is symmetric about its mean, u
The statement is true. The normal curve is a symmetric distribution with one peak, which means the mean, median, and mode are all equal. Therefore, the normal curve is symmetric about the mean, u.
In the binomial probability distribution function nCx represents the number of ways of obtaining x successes in n trials.
True
Probability is a measure of the likelihood of a random phenomenon or chance behavior.
True
When can the Empirical Rule be used to identify unusual results in a binomial experiment? Why can the Empirical Rule be used to identify results in a binomial experiment?
When the binomial distribution is approximately bell shaped, about 95% of the outcomes will be in the interval from mu minus 2 sigma to mu plus 2 sigma. The Empirical Rule can be used to identify results in binomial experiments when np( 1- p) greater than or equals 10.
The notation za is the z-score that the area under the standard normal curve to the right of za is
a
The factorial symbol, n!, is defined as n!
n(n-1) time 3time2times1 0!=1
The points at x =__ and x=_____ are the inflection points on the normal curve.
x-standard deviation/ x+standard deviation
According to a center for disease control, the probability that a randomly selected person has hearing problems is 0.142. The probability that a randomly selected person has vision problems is 0.089. Can we compute the probability of randomly selecting a person who has hearing problems or vision problems by adding these probabilities? Why or why not?
No, because hearing and vision problems are not mutually exclusive. So, some people have both hearing and vision problems. These people would be included twice in the probability.
7 cards are selected from a standard 52-card deck without replacement. The number of clubs selected is recorded. Binomial Experiment?
No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.
Determine if the following probability experiment represents a binomial experiment. 50 high school students asked about their weight?
No, this probability experiment does not represent a binomial experiment because the variable is continuous, and there are not two mutually exclusive outcomes.
When an event is almost certain to happen, its complement will be an unusual event.
True, the complement would be an unusual event.
An experimental drug is administered to 80 randomly selected individuals, with the number of individuals responding favorably recorded. Does the probability experiment represent a binomial experiment?
Yes, because the experiment satisfies all the criteria for a binomial experiment.
An investor randomly purchases 5 stocks listed on a stock exchange. Historically, the probability that a stock listed on this exchange will increase in value over the course of a year is 50%. The number of stocks that increase in value is recorded.
Yes, because the experiment satisfies all the criteria for a binomial experiment.
