Stat CH5
In the binomial probability formula, the variable x represents the _______.
In the binomial probability formula, the variable x represents the number of successes.
For the binomial distribution, which formula finds the standard deviation?
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A _______ random variable has infinitely many values associated with measurements.
A continuous random variable has infinitely many values associated with measurements.
In a probability histogram, there is a correspondence between _______.
In a probability histogram, there is a correspondence between area and probability.
The _______ of a discrete random variable represents the mean value of the outcomes.
The expected value of a discrete random variable represents the mean value of the outcomes.
Which of the following is not a requirement of the binomial probability distribution?
The trials must be dependent.
Which of the following is NOT one of the three methods for finding binomial probabilities that is found in the chapter on discrete probability distributions?
Use a simulation
Identify the expression for calculating the mean of a binomial distribution.
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A _______ random variable has either a finite or a countable number of values.
A discrete random variable has either a finite or a countable number of values.
A _______ variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
A random variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied. Treating 150 bald men with a special shampoo and recording how they say their scalp feels Choose the correct answer below.
No comma because there are more than two possible outcomes.
A main goal in statistics is to interpret and understand the meaning of statistical values. The _______ can be very helpful in understanding the meaning of the mean and standard deviation.
A main goal in statistics is to interpret and understand the meaning of statistical values. The Range Rule of Thumb can be very helpful in understanding the meaning of the mean and standard deviation.
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).
If calculations are time-consuming and if a sample size is no more than 5% of the size of the population, the 5% Guideline for Cumbersome Calculations states to treat the selections as being independent (even if the selections are technically dependent).
Based on a survey, assume that 57% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when five consumers are randomly selected, exactly three of them are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of getting three consumers comfortable with drones followed by two consumers not comfortable, as in this calculation: left parenthesis 0.57 right parenthesis left parenthesis 0.57 right parenthesis left parenthesis 0.57 right parenthesisleft parenthesis 0.43 right parenthesis left parenthesis 0.43 right parenthesisequals0.0342?
There are other arrangements consisting of three consumers who are comfortable and two who are not. The probabilities corresponding to those other arrangements should also be included in the result.
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.
Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a self-driving vehicle. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
yes .9 .8
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. Five hundred different voters in a region with two major political parties, A and B, are randomly selected from the population of 3.2 million registered voters. Each is asked if he or she is a member of political party A, recording Yes or No. Choose the correct answer below.
. Yes comma the result is a binomial probability distribution.
Refer to the accompanying table, which describes the number of adults in groups of five who reported sleepwalking. Find the mean and standard deviation for the numbers of sleepwalkers in groups of five.
The mean is 1.5 sleepwalker(s). The standard deviation is 1.0 sleepwalker(s).
Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births.
The mean is muequals 4 girl(s). The standard deviation is sigmaequals 1.4 girl(s).
The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls.
Use the range rule of thumb to identify a range of values that are not significant. The maximum value in this range is 8.3 girls. (Round to one decimal place as needed.) The minimum value in this range is 1.6 girls. (Round to one decimal place as needed.) Based on the result, is 1 girl in 10 births a significantly low number of girls? Explain. A. Yes, 1 girl is a significantly low number of girls, because 1 girl is below the range of values that are not significant.
Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Yes, the table shows a probability distribution. muequals 2.5 child(ren) sigmaequals 1.1 child(ren)
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 _______.
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.
n a state's Pick 3 lottery game, you pay $0.95 to select a sequence of three digits (from 0 to 9), such as 300. If you select the same sequence of three digits that are drawn, you win and collect $361.43. Complete parts (a) through (e).
a. How many different selections are possible? 1000 b. What is the probability of winning? 0.001 (Type an integer or a decimal.) c. If you win, what is your net profit? e. If you bet $ 0.95 in a certain state's Pick 4 game, the expected value is negative $ 0.59. Which bet is better, a $0.95 bet in the Pick 3 game or a $ 0.95 bet in the Pick 4 game? Explain. Neither bet is better because both games have the same expected value.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of hits to a website in a day b. The number of light bulbs that burn out in the next week in a room with 17 bulbs c. The gender of college students d. The number of points scored during a basketball game e. The number of free dash throw attempts before the first shot is made f. The amount of rain in City Upper B during April
a. It is a discrete random variable. b. It is a discrete random variable. c. It is not a random variable. d. It is a discrete random variable. e. It is a discrete random variable. f. It is a continuous random variable.
Based on a poll, 60% of adults believe in reincarnation. Assume that 6 adults are randomly selected, and find the indicated probability. Complete parts (a) through (d) below. calc binompdf
a. What is the probability that exactly 5 of the selected adults believe in reincarnation? The probability that exactly 5 of the 6 adults believe in reincarnation is 0.187. (Round to three decimal places as needed.) b. What is the probability that all of the selected adults believe in reincarnation? The probability that all of the selected adults believe in reincarnation is 0.047. (Round to three decimal places as needed.) c. What is the probability that at least 5 of the selected adults believe in reincarnation? The probability that at least 5 of the selected adults believe in reincarnation is 0.233. (Round to three decimal places as needed.) d. If 6 adults are randomly selected, is 5 a significantly high number who believe in reincarnation? No, because the probability that 5 or more of the selected adults believe in reincarnation is greater than 0.05.
The accompanying table describes the random variable x, the numbers of adults in groups of five who reported sleepwalking. Complete parts (a) through (d) below. Find the probability of getting exactly 4 sleepwalkers among 5 adults
c. Since the probability of getting 5 sleepwalkers includes getting 4 sleepwalkers, the result from part (b) is the relevant probability. d. Yes, since the appropriate probability is less than 0.05, it is a significantly high number.
The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts (a) through (d) below. Find the probability of getting exactly 1 girl in 8 births.
c. Since getting 0 girls is an even lower number of girls than getting 1 girl, the result from part (b) is the relevant probability. d. Yes, since the appropriate probability is less than 0.05, it is a significantly low number.
The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts (a) through (d) below.
c. Since the probability of getting 7 or 8 girls includes getting 6 girls, the result from part (b) is the relevant probability. d. No, since the appropriate probability is greater than 0.05, it is not a significantly high numbe
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. Five cards are selected from a standard 52-card deck without replacement. The number of fours selected is recorded. Does the probability experiment represent a binomial experiment?
No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.
Ted is not particularly creative. He uses the pickup line "If I could rearrange the alphabet, I'd put U and I together." The random variable x is the number of women Ted approaches before encountering one who reacts positively. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
No, the sum of all the probabilities is not equal to 1. The table does not show a probability distribution.
Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied. Recording the genders of 50 people in a statistics class nothing
A. Yes comma because all 4 requirements are satisfied.
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An experimental drug is administered to 160 randomly selected individuals, with the number of individuals responding favorably recorded. Does the probability experiment represent a binomial experiment?
A. Yes, because the experiment satisfies all the criteria for a binomial experiment.
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 0plus. What does 0plus indicate? Does 0plus indicate that it is impossible to get exactly 24 consumers who are comfortable with drones?
The probability 0plus indicates that the probability is a very small positive value. It indicates that the event is possible, but very unlikely.
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 50 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 6000 batteries, and 2% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? calc binompdf
The probability that this whole shipment will be accepted is 0.9216. (Round to four decimal places as needed.) The company will accept 92.16% of the shipments and will reject 7.84% of the shipments, so almost all of the shipments will be accepted.
Is the random variable given in the accompanying table discrete or continuous? Explain.
The random variable given in the accompanying table is discrete because there are a finite number of values.
For 100 births, P(exactly 55 girls)equals0.0485 and P(55 or more girls)equals0.184. Is 55 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question? Consider a number of girls to be significantly high if the appropriate probability is 0.05 or less.
The relevant probability is P(55 or more girls), so 55 girls in 100 births is not a significantly high number of girls because the relevant probability is greater than 0.05.
Based on a survey, assume that 28% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when four consumers are randomly selected, exactly two of them are comfortable with delivery by drones. Identify the values of n, x, p, and q
The value of n is 4. (Type an integer or a decimal. Do not round.) The value of x is 2. (Type an integer or a decimal. Do not round.) The value of p is 0.28. (Type an integer or a decimal. Do not round.) The value of q is 0.72. (Type an integer or a decimal. Do not round.)
Based on a survey, assume that 59% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when four consumers are randomly selected, exactly two of them 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 two consumers not comfortable, as in this calculation: left parenthesis 0.59 right parenthesis left parenthesis 0.59 right parenthesisleft parenthesis 0.41 right parenthesis left parenthesis 0.41 right parenthesisequals0.0585?
There are other arrangements consisting of two consumers who are comfortable and two who are not. The probabilities corresponding to those other arrangements should also be included in the result
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.
When conducting research on color blindness in males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Yes, the table shows a probability distribution muequals 0.4 male(s) sigmaequals 0.6 male(s)
A sociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied
Yes, the table shows a probability distribution. muequals 1.6 adult(s) sigmaequals 0.8 adult(s)
