Math 245 Homework - for midterm
Identify the sampling technique used. Based on 10,000 responses form 25,000 questionnaires sent to its alumni, a major university estimated that the annual salary of its alumni was $101,500 per year.
random
The mean score of a placement exam for entrance into a math class is 80, with a standard deviation of 10. Use the empirical rule to find the percentage of scores that lie between 60 and 80. (Assume the data set has a bell-shaped distribution.)
47.5%
Determine whether you would take a census or use a sampling. If you would use a sampling, decide what sampling technique you would use. The average age of the 80 residents of an assisted living center.
Census
One thousand tickets are sold at $5 each. One ticket will be randomly selected and the winner will receive a color television valued at $365. What is the expected value for a person that buys one ticket? Round the answer to the nearest cent.
-4.63
A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the student guesses on each question, what is the probability that the student will pass the test?
.055
Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a diamond and then selecting a club. The probability of selecting a diamond and then selecting a club is _______
.0637
In a study, 45% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 13 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 13 adults are randomly selected, 3 or fewer are in excellent health. Round to three decimal places.
.093
The national Education Association collects dat on the number of years of teaching experience of high-school teachers. A sample taken this year of 19 high-school teachers yielded the following data on number of years of teaching experience. Identify potential outliers, if any, for the given data. 16 22 1 34 15 5 18 8 20 14 17 19 16 10 21 28 14 38 18
1, 34 , 38
The heights (in inches) of 10 adult males are listed below. Find the sample standard deviation. Round to the nearest hundredth. 70 , 72 , 71 , 70 , 69 , 73 , 69 , 68 , 70 , 71
1.49
What is the difference between. census and a sampling?
A census includes the entire population. A sampling includes only part of the population.
Determine the written description of the complement of the given event. When 15 job applicants are tested for a certain ability, at least one of them tests positive. A. None of them test negative. B. More than one of them test negative. C. None of them test positive. D. All of the test positive.
C. Note : It is important to pay close attention to the language used to define the events. If at least one of them makes the team, then one or more students make the team. The complement of getting at least one of a particular type of item is getting none of that type of item. If one or more students make the team in the given event, the complement must be that zero students make the team. One way of writing zero students make the team is none of them make the team. Therefore, the complement of at least one of them makes the team is none of them make the team.
Decide whether the random variable x is discrete or continuous. Explain your reasoning. Let x represent the amount of rain (in inches) that fell this spring. Is the random variables x discrete or continuous? A. Continuous B. Discrete
Continuous
Use the Venn diagram to identify the population and the sample. BIG BOX : The ages of home owners in a certain state SMALL BOX : The ages of home owner in the state who work at home.
Correct description of the population : The ages of home owners in the state Correct description of the sample : The ages of home owners in the state who work at home
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. According to company records, the probability that a washing machine will need repairs during a ten-year period is 0.16. This is an example of _________ probability, since _________________.
Empirical The stated probability is calculated based on observations from the company records
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. More types of calculations can be preformed with data at the nominal level than with data at the interval level.
False. More types of calculations can be preformed with data at the interval level than with data at the nominal level.
Identify the data set's level of measurement. Number of milligrams of tar in 97 cigarettes
ratio
A study of 886 senior citizens shows that participants who exercise regularly exhibit less of a decline in the cognitive ability than those who barley exercise at all. From this study, a researcher infers that your cognitive ability increases the more you exercise. What is wrong with this type of reasoning? The inference _________________ imply that exercise _____________ a person's cognitive ability. The study shows ________________ in cognitive ability.
May incorrectly Increases A slower decline
The weight (in pounds) of 30 preschools children are listed below. Find the five-number summary. 25 25 26 26.5 27 27 27.5 28 28.5 29 29 30 30 30.5 31 31 32 32.5 32.5 33 33 34 34.5 35 35 37 37 38 38
Min = 25 Q1 = 28 Q2 = 30.75 Q3 = 34 Max = 38
The graph to the right shows the number of people that watch each sport in a local pub. Identify the level of measurement of the data listed on the horizontal and vertical axes in the figure. Identify the level of measurement of the data listed on the horizontal axis in the figure. Identify the level of measurement of the data listed on the vertical axis in the figure.
Nominal Ratio
Tye jersey numbers for players on a baseball team are listed below. Identify the level of measurement of the data set. Which is the data set's level of measurement?
Nominal. The data are categorized using numbers, but no mathematical computations can be made.
A physics class has 50 students. Of these, 10 students are physics majors and 18 students are female. Of the physics majors, three are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or
P(A or B) = P(A) + P(B) P(female or physics) = P(female) + P(physics) - P(female and physics) P (female) = number of females divided by total students : 18 / 50 = .36 P (physics) = number of physics majors divided by total students : 10 / 50 = .2 P(female and physics) = number of female physics major divided by total students : 3 / 50 = .06 P(female or physics) = P(female) + P(physics) - P(female and physics) : (18/50) + (10/50) - (3/50) : .36 +.2 - .06 = .5
Determine whether the underlined value is a parameter or a statistic. The average score of 28 students taking a calculus midterm exam was 72%. Is the value a parameter or a statistic?
Parameter
Identify the population and the sample. Describe the sample data set. A survey of 132 law firms in a country found that the average hourly billing rate for partners was $558.
Population : All the firms in the country Sample : The law firms that were surveyed Sample data set : The average hourly bill rate for partners of 132 law firms was $558
What is a replication in an experiment? Why is replication important?
Replication is repetition of an experiment under the same or similar conditions. Replication is important because it enhances the validity of the results.
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. In a survey of a sample of 1050 teenager, 17% said they like to watch soccer.
Statistic, because the data set of a simple of 1050 teenagers is a sample.
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. An analyst feels that a certain stock's probability of decreasing in price over the next week is 0.77. This is an example of ___________ probability, since __________________.
Subjective The stated probability is most likely based on intuition, an educated guess, or an estimate.
Identify the sampling technique used. Thirty-five sophomores, 43 juniors and 48 seniors are randomly selected form 333 sophomores, 592 juniors and 483 seniors at a certain high school
statified
Identify the sampling technique used. A researcher randomly selects and interviews fifty male and fifty female teachers
stratified
Identify the sampling technique used. Every fifth person boarding a plane is searched thoroughly.
systematic
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. A placebo is an actual treatment.
The statement is false. A placebo is a fake treatment.
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. A double-blind experiment is used to increase the placebo effect.
The statement is false. Double blinding is used to decrease the placebo effect.
What is the difference between a random sample and a simple random sample?
With a random sample, each individual has the same chance of being selected. With a simple randomsample, all samples of the same size have the same chance of being selected.
Identify the sampling technique used. At a local community college, five statistics classes are randomly selected out of 20 and all students form each class are interviewed.
cluster
Identify the sampling technique used. A community college student interviews everyone in a statistics class to determine the percentage of students that own a car.
convenience
In the game of roulette, a player can place a $10 bet on the number 30 and have a 1/38 probability of winning. If the metal ball lands on 30, the player gets to keep the $10 paid to play the game and the player is awarded an additional $350. Otherwise, the player is awarded nothing and the casino takes the player's $10. 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.
create a table 1. x = given (winning/losing) 2. P(x) = probability of win or lose 3. xP(x) = x time P(x) Add xP(x) -.53
Match the description of the sample with the correct plot. Time (in minutes) it takes a sample of employees to drive to work.
dot graph thing starting from 5 to 45
Determine whether the study depicts an observational study or an experiment. A medical researcher obtains a sample of adults suffering from diabetes. She randomly assigns 71 people to a treatment group and 71 to a placebo group. The treatment group receives a medication over a period of three months and the placebo group receives a placebo over the same time frame. At the end of three months thepatients' symptoms are evaluated.
experiment
Identify the data set's level of measurement. Temperatures of 61 selected refrigerators
interval
Identify the data set's level of measurement. Marriage status (married, single, or divorced) of the faculty at a university
nominal
Identify the level of measurement of the data listed on the horizontal axis in the graph Five top selling vehicles
nominal
Decide if the events A and B are mutually exclusive or not mutually exclusive. A date in Philadelphia is selected. A: It rains that day. B: It snows that day.
not mutually exclusive
You are asked to compare three data sets. Without calculating, determine which data set has the greatest sample standard deviation and which has the least sample standard deviation.
Greatest sample standard deviation (i) Least sample standard deviation (iii)
What is the difference between an observational study and an experiment?
In an experiment, a treatment is applied to part of a population and responses are observed. In an observational study, a researcher measures characteristics of interest of a part of a population but does not change existing conditions.
In a poll, 1,002 men in a country were asked whether they favor oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos. "Among the respondents, 48% said that they were in favor. Identify the population and the sample.
Population in the given problem : All men in the country Sample in the given problem : The 1,002 men selected
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Guessing the last digit in the price of a TV Sample Space : Outcomes :
Sample space : 0,1,2,3,4,5,6,7,8,9 Outcomes : 10
Which of the following is not a requirement of the binomial probability distribution?
The trials must be dependent
25 of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select a DVR that is not defective?
100-25 75 divided by 100 .75
Approximate the mean of the grouped data. Round to the nearest whole number. Weight | Frequency 135-139 | 16 140-144 | 19 145-149 | 20 150-154 | 10 155-159 | 15
146
Find the sample standard deviation. Round to the nearest tenth. 15 , 42 , 53 , 7 , 9 , 12 , 14 , 28 , 47
17.8
Approximate the mean of the grouped date. Round to the nearest whole number Phone calls | Frequency 8-11 | 33 12-15 | 23 16-19 | 47 20-23 | 22 24-27 | 34
18
Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most three boys in ten births.
.172
A recent survey found that 70% of all adults over 50 wear glasses for driving. In a random sample of 10 adults over50, what is the probability that at least six wear glasses?
.85
The salaries of a random sample of a company's employees are summarized in the frequency distribution below. Approximate the sample mean using the grouped data formulas. Salary | Employees 5,001-10,000 | 16 10,001-15,000 | 10 15,001-20,000 | 20 20,001-25,00 | 15 25,001-30,000 | 19
18,188.00
The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find Q1 154 156 165 165 170 171 172 180 184 185 189 189 190 192 195 198 198 200 200 200 205 205 211 215 220 220 225 238 255 265
180
Use the given frequency distribution to find the Class width Class midpoint of the first class Class boundaries of the first class Class / Frequency 50-52 / 5 53-55 / 8 56-58 / 12 59-61 / 13 62-64 / 11
2 51 49.5-52.5
You randomly select an integer from 0 to 19 (inclusively) and then randomly select an integer from 0 to 39 (inclusively). What is the probability of selecting a 14 both times?
20 x 40 = 800 1 / 800 .00125
For the following data set, approximate the sample standard deviation to the nearest hundredth using the grouped data formulas. Height | Frequency 50-52 | 5 53-55 | 8 56-58 | 12 59-61 | 13 62-64 | 11
3.85
Suppose a survey of 968 major-appliance shoppers found that more than 31% bought extended warranties. Which part of the survey represents the descriptive branch of statistics? Make an inference based on the results of the survey. Choose the best statement of the descriptive statistic in the problem. Choose the best inference from the given information.
31% of major-appliance shoppers in the same bought extended warranties. Most major-appliance shoppers do not buy extended warranties.
The mean SAT verbal score is 463, with a standard deviation of 92. Use the empirical rule to determine what percent of the scores lie between 371 and 463. (Assume the data set has a bell-shaped distribution.)
34%
The test scores of 15 students are listed below. Identify potential outliers, if any, for the given data. 38 , 47 , 55 , 65 , 67 68 , 70 , 72 , 74 , 77 80 , 82 , 87 , 90 , 99
38
The access code for a garage door consists of three digits. Each digit can be any number from 1 through 8, and each digit can be repeated. Complete parts (a) through (c). (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? Round to three decimal places
8 x 8 x 8 = 512 A . 512 1 / 512 = .00195 B. .002 1 - .002 = .998 C. .998
Use the ogive to the right to approximate the sample size 28 80 341 100
80
A student receives test scores of 62, 83, and 91. The student's final exam score is 88, and homework score is 76. Each test is worth 20% of the final grade, the final exam is 25% of the final grade, and the homework grade is 15% of the final grade. What is the student's final grade in the class?
80.6
The mean IQ score of adults is 100, with a standard deviation of 15. Use the empirical rule to find the percentage of adults with scores between 70 and 130. (Assume the data set has a bell-shaped distribution)
95%
The mean score of a competency test is 71, with a standard deviation of 6. Use the empirical rule to find the percentage of scores between 59 and 83. (Assume the data set has a bell-shaped distribution.)
95%
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. If two events are independent, P(A|B)=P(B). A. False; if events A and B are independent, then P(A and B)=P(A)•P(B). B. False; if events A and B are independent, then P(B|A)=P(A). C. True D. False; if events A and B are independent, then P(A and B)=0.
A
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is greater than 0.5. A. The statement is false. The correct statement is "You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is exactly 0.5." B. The statement is false. The correct statement is "You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is less than 0.5." C. The statement is false. The correct statement is "You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is 1." D. The statement is false. The correct statement is "You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth flip is 0." E. The statement is true.
A
If two events are mutually exclusive, why is P(A and B)=0? A. P(A and B)=0 because A and B cannot occur at the same time. B. P(A and B)=0 because A and B are complements of each other. C. P(A and B)=0 because A and B are independent. D. P(A and B)=0 because A and B each have the same probability.
A
The following table contains data from a study of two airlines which fly to Small Town, USA. If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on time given that it was an Upstate Airlines flight. Express your answer as a simplified fraction. A. 43/48 B. 43/87 C. 11/76 D. none
A
What does the notation P(B|A) mean? A. The probability of event B occurring, given that event A has occurred B. The probability of event B occurring, divided by the probability of event A occurring C. The probability of both event A and event B occurring D. The probability of event A occurring, given that event B has occurred
A
What is the difference between an outcome and an event? A. An outcome is the result of a single probability experiment. An event is a set of one or more possible outcomes. B. An outcome is the result of a single probability experiment. An event is the set of all possible outcomes. C. An event is the result of a single probability experiment. An outcome is the set of all possible events. D. An event is the result of a single probability experiment. An outcome is a set of one or more possible events.
A
What is the difference between independent and dependent events? A. Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event. B. Two events are independent if they can occur at the same time. Two events are dependent if only one of the two events can occur. C. Two events are independent when the occurrence of one event affects the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event does not affect the probability of the occurrence of the other event. D. Two events are independent if only one of the two events can occur. Two events are dependent if they can occur at the same time.
A
Determine which numbers could not be used to represent the probability of an event. A. 64/25 because probability values cannot be greater than 1. B. 0, because probability values must be greater than 0. C. 33.3%, this is because probability values cannot be greater than 1. D. 320/1058, because probability values cannot be in fraction form. E. −1.5, because probability values cannot be less than 0. F. 0.0002, because probability values must be rounded to two decimal places.
A & E
In a recent study on the effects of sleep and test results, volunteers took a math test. The volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on the math test than were sleep-deprived volunteers. Complete parts a through d. A. Identify the sample used in the study. B. What is the samples population? C. Which part of the study represents the descriptive branch of statistics? D. Make an inference based on the results of the study.
A) The sample is the test results of the volunteers in the study. B) The population is the collection of the test results of all individuals who might ever complete the math test. C) The statement "three times more likely to answer questions correctly" is an example of descriptive statistics D) Individuals who are not sleep deprived will be more likely to answer math questions correctly than individuals who are sleep deprived.
Determine whether the variable is a quantitative. Explain your reasoning. Favorite sport Is the variable qualitative or quantitative?
The variable is qualitative because a favorite sport describes an attribute or characteristic.
The table below shows the results of a survey that asked 2853 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (d). A. Find the probability that the person is frequently or occasionally involved in charity work. P (being frequently involved or being occasionally involved) = ________ B. Find the probability that the person is female or not involved in charity work at all. P (being female or not being involved) C. Find the probability that the person is male or frequently involved in charity work. P(being male or being frequently involved.) D. Find the probability that the person is female or not frequently involved in charity work. P(being female or not being frequently involved.)
A. P(A orB) = P(A) + P(B) P(A) = Frequently total divided by total total : 427 / 2853 = .150 P(B) = Occasionally total divided by total total : 891 / 2853 = .312 P(A or B) = (427/2853) + (891/2853) = .150 +.312 = .462 B. P(A or B) = P(A) + P(B) - P(A and B) P(A) = Female total divided by total total : 1382 / 2853 = .484 P(B) = Not at all total divided by total total : 1535 / 2853 = .538 P(A and B) = Not at all female divided but total total : 741 / 2853 = .260 P(A or B) = (1382/2853) + (1535/2853) - (741/2853) = .484 + .538 - .260 = .762 C. P(A or B) = P(A) + P(B) - P(A and B) P(A) = Male total divided by total total : 1471 / 2853 = .516 P(B) = frequently total divided by total total : 427 / 2853 =.150 P(A and B) = frequently male divided by total total : 226 / 2853 = .079 P(A or B) = (1471/2853) + (427/2853) - (226/2853) = .516 + .150 - .079 = .587 D. P(A or B) = P(A) + P(B) - P(A and B) P(A) = Female total divided by total total : 1382 / 2853 = .484 P(B) = (Occasionally total + not at all total) divided by total total : (891 + 1535) / 2853 = .85 P(A and B) = (Occasionally female + not at all female) divided by total total : (440 + 741) / 2853 = .414 P(A or B) = (1382/2853) + [(891+1535) / 2853] - [(440+741) /2853] = .484 + .85 - .414 = .92
The data given below show the number of overtime hours worked in one week per employee. Use the data to complete parts (a) and (b). OT = Employee 0=5 1=12 2=31 3=55 4=46 5=28 6=18
A. add total employees divided by employee for each overtime category employees for overtime category (5) divided by total employees (195) and so on .026 , .062 , .159 , .282 , .236 , .144 , .092 C. approximately symmetric but not uniform
The accompanying table shows the numbers of male and female students in a particular country who receivedbachelor's degrees in business in a recent year. Complete parts (a) and (b) below. Click the icon to view the data on business degrees. (a) Find the probability that a randomly selected student is male, given that the student received a business degree. The probability that a randomly selected student is male, given that the student received a business degree, is _____ (b) Find the probability that a randomly selected student received a business degree, given that the student is female. The probability that a randomly selected student received a business degree, given that the student is female, is ____ Round to 3rd decimal place
A. males w business degree divided by total of business degree A. 189,647 / 362,309 = .523 B. females w business degree divided by total females B. 172,662 / 1,071,734 = .161
What is an inherent zero? Describe three examples of data sets that have inherent zeros and three that do not. Choose the correct answer below : Select three examples of data sets that have inherent zeros below : Select three examples of data sets that do not have inherent zeros below :
An inherent zero is a zero that implies none Average age of college students in years. Maximum wind speed during a hurricane. Average monthly precipitation in inches. Temperature in degree Fahrenheit. Average IQ score of a high school class. A student's level of happiness measured from 0 to 10.
A question has five multiple-choice answers. Find the probability of guessing an incorrect answer. A. 3/5 B. 4/5 C. 5/2 D. 1/5
B
Determine whether the statement is true or false. You toss a coin and roll a die. The event "tossing tails and rolling a 3 or 5" is a simple event. Determine the most appropriate conclusion. A. False, the event is not simple because it requires the probability of the coin and the probability of the die to be calculated. B. False, the event is not simple because it consists of two possible outcomes. C. True, the event is simple since the coin will land on tails 50% of the time. D. True, the event is simple because only one condition in the event needs to be met.
B
The following table contains data from a study of two airlines which fly to Small Town, USA. If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight which was on time. Express your answer as a simplified fraction. A. 11/76 B. 43/87 C. 43/76 D. none
B
Which of the following cannot be a probability? Question content area bottom Part 1 A. ^-6/3 B. −76 C. 0.001 D. 0
B
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram. Determining an athlete's sport (baseball (B), soccer (S), football (F)) and skill (low (L), medium (M), high (H)) Sample Space A. {BL, BM, SL, SM, FL, FM, FL, FM, BL, BM} B. {BL, BM, BH, SL, SM, SH, FL, FM, FH} C. {BL, BM, SL, SM, FL, FM} D. {BL, BM, BH, SL, SM, SH, FL, FM, FH, FL, FM, FH}
B Outcomes : 9
Determine whether the statement is true or false. When an event is almost certain to happen, its complement will be an unusual event. A. False, the probability of the complement has no relation to the probability of the event. B. False, the probability of the complement will have a higher probability than the event. C. True, the complement would be an unusual event. D. False, the complement of an event has an equal probability as the event.
C
The following table contains data from a study of two airlines which fly to Small Town, USA. If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight given that it was late. Express your answer as a simplified fraction. A. 5/48 B. 5/87 C. 5/11 D. none
C
Choose the three formulas that can be used to describe complementary events. Select the three formulas that can be used to describe complementary events. A. P(E)=1/P(E') B. P(E')=1/P(E) C. P(E')=1−P(E) D. P(E)+P(E')=1 E. P(E)/P(E')=1 F. P(E)−P(E')=1 G.P(E)=1−P(E')
C , D , G
Determine whether the distribution is a discrete probability distribution. A. Yes, because the distribution is symmetric B. No, because some of the probabilities have values greater than 1 or less than 0. C. No, because the total probability is not equal to 1. D. Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.
D
Explain how the complement can be used to find the probability of getting at least one item of a particular type. A. The complement of "at least one" is "all." So, the probability of getting at least one item is equal to 1−P(all items). B. The complement of "at least one" is "all." So, the probability of getting at least one item is equal to P(all items)−1. C. The complement of "at least one" is "none." So, the probability of getting at least one item is equal toP(none of the items)−1. D. The complement of "at least one" is "none." So, the probability of getting at least one item is equal to 1−P(none of the items).
D
Determine whether the events are independent or dependent. Explain your reasoning. Returning a rented movie after the due date and receiving a late fee The events are ________ because the outcome of returning a rented movie after the due date __________ the probability of the outcome of receiving a late fee.
Dependent Affects
What are two main branches of statistics?
Descriptive statistics and inferential statistics
Decide whether the random variable x is discrete or continuous. x represents the total number of die rolls required for an individual to roll a five. Continuous or Discrete
Discrete
Use the probability distribution to complete parts a and b below A. Find the mean, variance, and standard deviation
MEAN - - x = given - P(x) = given - x(P(x) = multiple both Mean = sum of xP(x) = VARIANCE - 1. X= given 2. P(x) = given 3. x-U = take x and subtract the mean 4. (x-U)^2 = square 3. 5. (x-u)^2P(x) = multiply 4 and 2 Variance = sum of 5th column Standard Deviation = square root of variance
From the stem-and-leaf plot below, what is the maximum and what is the minimum entry. Key : 11 | 7 = 11.7
Max : 17.8 Min : 11.1
Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Choosing 3 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time without replacement, keeping track of the number of red marbles chosen.
Not binomial - the trials are not independent
Identify the sampling techniques used, and discuss the potential sources of bias (if any). Explain. In 1965, researchers used random digit dialing to call 900 people and ask what obstacles kept them from attending town hall meetings. What type of sampling was used? What potential sources of bias were present, if any?
Simple random sampling was sued, since each number had an equal chance of being dialed, so all samples of 900 phone numbers had an equal chance of being selected. Individuals may have refused to participate in the sample. This may have made the sample less representative of the population. Telephone sampling only includes people who had telephones. People who owned telephones may have been older or wealthier on average, and may not have been representative of the entire population. Individuals may have not been available when researchers were calling. Those individuals that were available may have not been representative of the population.
Identify the sampling techniques used. A lobbyist for a major airspace firm assigns a number to each legislator and then uses a computer to randomly generate ten numbers. The lobbyist contacts the legislators corresponding to these numbers.
random
Identify the data set's level of measurement. numbers of touchdowns scored by a major university in five randomly selected games 4, 4, 2, 4, 2
ratio
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Times to run 100 meters. The variable is ________________ because times are _________________.
quantitative numerical measurements
