Stat CH5 |44 questions and answers

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. 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. 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. 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. 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​ _______ 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. ​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. 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. 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) 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) 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. 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) ​ 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 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). 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). 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. 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.) 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. 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. Which of the following is not a requirement of the binomial probability​ distribution? The trials must be dependent. 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). In the binomial probability​ formula, the variable x represents the​ _______. In the binomial probability​ formula, the variable x represents the number of successes. 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 For the binomial​ distribution, which formula finds the standard​ deviation? //npq 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. Identify the expression for calculating the mean of a binomial distribution. np 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 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