Chapter5
Four requirements of Binomial Distribution
1. The procedure has a fixed number of trials. (A trial is a single observation.) 2. The trials must be independent, meaning that the outcome of any individual trial doesn't affect the probabilities in the other trials. 3. Each trial must have all outcomes classified into exactly two categories, commonly referred to as success and failure. 4. The probability of a success remains the same in all trials.
Fill in the blank. If calculations are time-consuming and if a sample size is no more than 5% of the size of the population, the _______ states to treat the selections as being independent (even if the selections are technically dependent).
5% Guideline for Cumbersome Calculations
Fill in the blank. In a probability histogram, there is a correspondence between _______.
Area and Probability -Explanation: In a probability histogram, there is a correspondence between area and probability because the areas of the rectangles in a probability histogram are the same as the probabilities of the relative frequencies.
Fill in the blank. A _______ random variable has infinitely many values associated with measurements.
Continuous
Fill in the blank. A _______ random variable has either a finite or a countable number of values.
Discrete
Fill in the blank. The _______ of a discrete random variable represents the mean value of the outcomes.
Expected Value Explanation: The expected value is the average value that we would expect to get if the trials could continue indefinitely.
Determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). If the procedure is not binomial, identify at least one requirement that is not satisfied.Eightifferent senators from the current U.S. Congress are randomly selected without replacement and whether or not they've served over 2 terms is recorded.
No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.
Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied. Treating 20 bald men with a special shampoo and recording how they say their scalp feels
No, because there are more than two possible outcomes.
Multiple-choice questions each have five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to three such questions.
P(CWW)=(.2)(.8)(.8) c. Based on the preceding results, what is the probability of getting exactly one correct answer when three guesses are made? 3*.128=.384
A _______ variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
Random Variable -Explanation: A random variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure. Next Question
Fill in the blank. If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct. This represents the _______.
Rare Event Rule
Which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births: the result from part (a) or part (b)?
Since getting 0 girls is an even lower number of girls than getting 1 girl, the result from part (b) is the relevant probability.
Based on a survey, when 1009 consumers were asked if they are comfortable with drones delivering their purchases, 42% said yes. The probability of randomly selecting 30 of the 1009 consumers and getting exactly 24 who are comfortable with the drones is represented as 0 +.What does 0 + indicate? Does 0 +indicate that it is impossible to get exactly 24 consumers who are comfortable with drones?
The probability 0 +indicates that the probability is a very small positive value. It indicates that the event is possible, but very unlikely.
Is the random variable given in the accompanying table discrete or continuous? Explain. 0 | 0.063 1 | 0.250 2 | 0.375 3| 0.250 4 | 0.063
The random variable given in the accompanying table is discrete because there are a finite number of values.
The table to the right lists probabilities for the corresponding numbers of girls in three births. What is the random variable, what are its possible values, and are its values numerical?
The random variable is x, which is the number of girls in three births. The possible values of x are 0, 1, 2, and 3. The values of the random value x are numerical.
Which of the following is not a requirement of the binomial probability distribution?
The trials must be dependent.
Based on a survey, assume that 444% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when six onsumers are randomly selected, exactly two of hem are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of getting two consumers comfortable with drones followed by four consumers not comfortable, as in this calculation: (.44)(.44)(.56)(.56)(.56)=.0190
There are other arrangements consisting of two consumers who are comfortable and fourwho are not. The probabilities corresponding to those other arrangements should also be included in the result.
Determine whether or not the procedure described below results in a binomial distribution. If it is not binomial, identify at least one requirement that is not satisfied.Seven hundred different voters in a region with two major political parties, A and B, are randomly selected from the population of 2.4 million registered voters. Each is asked if he or she is a member of political party A, recording Yes or No.
Yes comma the result is a binomial probability distribution.
Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied. Determining whether each of 20 mp 3 players is acceptable or defective.
Yes, because all 4 requirements are satisfied.
A Gallup poll of 1236 adults showed that 12% of the respondents believe that it is bad luck to walk under a ladder. Consider the probability that among 30 randomly selected people from the 1236 who were polled, there are at least 2 who have that belief. Given that the subjects surveyed were selected without replacement, the events are not independent. Can the probability be found by using the binomial probability formula? Why or why not?
Yes. Although the selections are not independent, they can be treated as being independent by applying the 5% guideline. Only 30 people are randomly selected from the group of 1236, which is less than 5%.
Determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). If the procedure is not binomial, identify at least one requirement that is not satisfied. The YSORT method of gender selection, developed by the Genetics & IVF Institute, was designed to increase the likelihood that a baby will be a boy. When 160 couples use the YSORT method and give birth to 160 babies, the genders of the babies are recorded.
Yes, because the procedure satisfies all the criteria for a binomial distribution.
Is 1 a significantly low number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event.
Yes, since the appropriate probability is less than 0.05, it is a significantly low number.
