stat exam 4 SG
Is the expected value of the probability distribution of a random variable always one of the possible values of x? Explain.
No, because the expected value may not be a possible value of x for one trial, but it represents the average value of x over a large number of trials.
The following histograms each represent binomial distributions. Each distribution has the same number of trials n but different probabilities of success p. Match p equals 0.3, p equals 0.5, p equals 0.6 with the correct graph.
(a) p equals 0.3, (b) p equals 0.5, (c) p equals 0.6
A frequency distribution is shown below. Complete parts (a) and (b). The number of televisions per household in a small town Televisions 0 1 2 3 Households 22 444 729 1407 (a) Use the frequency distribution to construct a probability distribution.
0 .008 1 .171 2 .280 3 .541 skewed left
What is a discrete probability distribution? What are the two conditions that determine a probability distribution? What is a discrete probability distribution? Choose the correct answer below. What are the two conditions that determine a probability distribution? Choose the correct answer below.
A discrete probability distribution lists each possible value a random variable can assume, together with its probability. 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 expected value of an accountant's profit and loss analysis is 0. Explain what this means.
An expected value of 0 means that the average money gained is equal to the average money spent, representing the break-even point.
Decide whether the random variable x is discrete or continuous. Explain your reasoning. Let x represent the volume of blood drawn for a blood test.
Continuous, because x is a random variable that cannot be counted.
Decide whether the graph represents a discrete random variable or a continuous random variable. home attendance at a football game
Discrete, because home attendance is a random variable that is countable.
Decide whether the graph represents a discrete random variable or a continuous random variable. Explain your reasoning. annual traffic in country
Discrete, because home attendance is a random variable that is countable.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. In most applications, continuous random variables represent counted data, while discrete random variables represent measured data.
False. In most applications, discrete random variables represent counted data, while continuous random variables represent measured data.
What is the significance of the mean of a probability distribution?
It is the expected value of a discrete random variable.
Using the data given below, determine whether it would unusual for a household to have no HD televisions. The number of televisions (HD) per household in a small town
It would be unusual because the probability of having no HD televisions is less than 0.05.
Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.13 1 0.27 2 0.18 3 0.27 4 0.13 Is the distribution a discrete probability distribution? Why? Choose the correct answer below.
No comma because the total probability is not equal to 1.
Determine whether the distribution is a probability distribution. x 0 1 2 3 4 5 P(x) StartFraction 1 Over 25 EndFraction
No comma because the total probability is not equal to 1.
A state lottery randomly chooses 6 balls numbered from 1 through 36 without replacement. You choose 6 numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If so, identify a success, specify the values n, p, and q and list the possible values of the random variable x.
No, because the probability of success is different for each trial. The experiment is not binomial. The experiment is not binomial. The experiment is not binomial.
What is a random variable? Choose the correct answer below.
The outcome of a probability experiment is often a count or a measure. When this occurs, the outcome is called a random variable.
Determine whether the random variable x is discrete or continuous. Explain. Let x represent the number of hits to a website in a day.
The random variable is discrete, because it has a countable number of possible outcomes.
Determine if the statement is true or false. If the statement is false, rewrite it as a true statement. The expected value of a random variable can never be negative.
The statement is false. The expected value of a random variable can be negative.
Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.09 1 0.21 2 0.40 3 0.21 4 0.09 Is the distribution a discrete probability distribution? Why? Choose the correct answer below.
Yes comma because the probabilities sum to 1 and are all between 0 and 1 comma inclusive.
Complete parts (a) and (b) below. The number of dogs per household in a small town Dogs 0 1 2 3 4 5 (a) Find the mean, variance, and standard deviation of the probability distribution. Find the mean of the probability distribution.
mean: variance: SD: probability:
About 30% of babies born with a certain ailment recover fully. A hospital is caring for five babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.
yes baby recovers n = 5 (# babies) p=.3 (30%) q = .7 (1-p) 0,1,2,3,4,5
In a binomial experiement, what does it mean to say that each trial is independent of the other trials?
Each trial is independent of the other trials if the outcome of one trial does not affect the outcome of any of the other trials.
Match n equals 4 comma n equals 8 comma n equals 12 with the correct graph. Each histogram shown below represents part of a binomial distribution. Each distribution has the same probability of success p but different numbers of trials n.
a.)12 : x axis b.) 4 c.) 8 What happens as the value of n increases and the probability of success remains the same? As n increases, the distribution becomes more symmetric.
33% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
cg
54% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
cg
In the game of roulette, a player can place a $9 bet on the number 22 and have a StartFraction 1 Over 38 EndFraction probability of winning. If the metal ball lands on 22, the player gets to keep the $9 paid to play the game and the player is awarded an additional $315. Otherwise, the player is awarded nothing and the casino takes the player's $9. Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose.
-.47
32% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles. Complete parts (a) through (c) below.
cg skewed right The values x equals 6 and xequals 5 would be unusual because their probabilities are less than 0.05.
48% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.
p(5)= .246 p(>6) = .107960 p(8) =.038897
A survey asks 2000 workers, "Has the economy forced you to reduce the amount of vacation you plan to take this year?" Thirty-three percent of those surveyed say they are reducing the amount of vacation. Thirty workers participating in the survey are randomly selected. The random variable represents the number of workers who are reducing the amount of vacation. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.
yes Selecting a worker who is reducing the amount of vacation n=30 p= .33 q=.67 x= 0 - 30
