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.