# Probability Questions and Answers

Statistics

ProbabilityJim is competing on a game show He has 6 number tiles in front of him that he has to put in order to create the price of a house The tiles he has are a 1 2 3 6 7 and 8 What is the probability that he guesses the price of the house correctly if he gets one guess For example he can choose the combination 723168 guessing that the house is 723 168 or he could choose the combination 187632 guessing that the car is 187 632 etc Select one O a 1 720 Ob 1 2840 O c 1 288 O d 1 3125

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ProbabilityWhat is the conditional probability that you will randomly select a blue shirt if there are 15 000 shirts Of those shirts 5 000 are blue Select one O a 5 15 O b 1 6 O c 1 3 O d 1 5

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ProbabilityIf you randomly select a sales receipt what is the probability that the customer ordered a hot dog and a soda Assume that there are 400 total sales Hot Dog Pizza No Food Total Concession Stand Sales Soda Water No Drink 50 62 120 58 30 20 200 140 46 4 10 60 Total 158 182 60 400

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ProbabilityThe University of Chicago s General Social Survey asked a representative sample of adults this question Which of the following statements best describes how your daily work is organized 1 I am free to decide how my daily work is organized 2 I can decide how my daily work is organized within certain limits 3 I am not free to decide how my daily work is organized Here is a two way table of the responses for three levels of education Response 1 2 3 Less than high school 31 49 Round your answer to 3 decimal places Leave your answer in decimal form Education level 47 P I am free to decide how my daily work is organized High School High school 161 269 112 a Choose an individual from the sample at random If the individual s education level was high school what is the probability that his or her response was I am free to decide how my daily work is organized Bachelor s 81 85 14 b Find the probability that Response 3 is given among those whose highest degree is less than a high school diploma Then find the probability that Response 3 is given among those whose highest degree is not less than a high school diploma

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ProbabilityWhich mineral can be found in rocks such as granite and is also present in most sedimentary rocks O a Olivine O b Quartz O c Muscovite O d Biotite

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ProbabilityQuestion 5 B Question 6 C D Question 7 P Bob is gathering eggs Bob has fed the chickens NOTE Click here for info on typing symbols and formulae in activities Bob has fed the ducks The ducks are playing in the pond It s not the case both that the ducks are playing in the pond and that Bob is gathering eggs P B If Bob has fed either the chickens or the ducks then the ducks are playing in the pond Cv D P It s not the case that if Bob has fed the chickens then the ducks are playing in the pond C P 2 poin 2 points 2 points

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Probabilitylocal fast food restaurant is running a Draw a three get it free lunch promotion After each Lustomer orders a touch screen display shows the message Press here to win a free lunch A computer program then simulates one card being drawn at random from a standard deck of laying cards If the chosen card is a 3 the customer s order is free Note that the probability of rawing a 3 from a standard deck of playing cards is 4 52 Otherwise the customer must pay the ill Suppose that 250 customers place lunch orders on the first day of the promotion Let X the umber of people who win a free lunch n 250 P 0 1 0 09 0 08 0 07 0 06 1 13 Plot distribution 1 One of the customers is surprised when only 10 people win a free lunch on a particular day Find the probability that 10 or fewer people win a free lunch by chance alone Show your work

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Probabilitycision The owner of the Sydney Construction Company must decide among building a condo constructing a shopping centre or leasing all the company s equipment to another company The profit that will result from each alternative will be determined by whether material costs remain stable increase moderately or increase significantly In the payoff table below the estimated profits losses are given in thousands Condo Shopping Centre Leasing Stable 1810 600 2150 Material Costs Moderate Increase 1040 600 750 Significant Increase 180 O Decision Shopping Centre based on 1733 max 1010 633 1733 O Decision Condo based on 1335 max 1335 950 300 O Decision Condo based on 890 max 890 633 200 O Decision Stable based on 1520 max 1520 797 593 O Decision Condo based on 2670 max 2670 1900 600 700 2300 ermine the best decision using the Equal likelihood Laplace decision criterion and to the nearest integer

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ProbabilityA random experiment consists of rolling two fair 7 sided dice a red die and a blue die each die has 7 sides listed from 1 to 7 Consider the following events A The sum of rolled outcomes is an odd number B At least one of the die s outcomes is a 1 P A If rounding use at least four digits after the decimal in your answer P A If rounding use at least four digits after the decimal in your answer P An B If rounding use at least four digits after the decimal in your answer P A n B If rounding use at least four digits after the decimal in your answer P AUB If rounding use at least four digits after the decimal in your answer

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ProbabilitySuppose a die has been loaded so that a six is scored four times more often than any other score while all the other scores are equally likely Express your answers to three decimals Part a What is the probability of scoring a two Part b What is the probability of scoring a six

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Probabilityb Using computer software compare 2018 sales to 2019 sales for each manufacturer by computing the percentage change in sales Make a list of the manufacturers in order of increasing percentage changes Which manufacturers are in the top five in percentage change Which manufacturers are in the bottom five in percentage change Enter values in decreasing order and negative values with a minus sign Round percentage answers to 2 decimal places

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ProbabilityIn the example scatterplot of child reading score as a function of child IQ score the correlation coefficient r out out oot 06 Child s reading test score 40 0 0 09 05 OF of of 90 115 120 125 130 135 140 145 150 Child s IQ test score 95 100 105 110 O is noticeably affected by the outlier of the relationship O has a negative value indicating an inverse linear relationship between reading score and IQ score O is close to zero indicating a lack of association volue because of the nonlinear pattern

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ProbabilityA partially completed yet still functional slot machine has two slots After the push of a button each slot on the machine will show one of the five following pictures a cherry a banana a lemon a horseshoe or a star Define the following events A exactly one cherry appears B exactly two lemons appears C at least one non fruit appears Part a How many elements are in this sample space There is no need to list them If rounding use at least four digits after the decimal in your answer Part b List the elements in A and find P A Similarly list the elements in B and find P B Part c Find P C If rounding use at least four digits after the decimal in your answer If rounding use at least four digits after the decimal in your answer If rounding use at least four digits after the decimal in your answer Part d What is the probability that exactly one cherry will appear and exactly two lemons will appear answer Part e What is the probability that exactly two lemons will appear or exactly one cherry will appear answer Part f Are A and B mutually exclusive events If rounding use at least four digits after the decimal in your If rounding use at least four digits after the decimal in your

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ProbabilityI asked loo Families about how members do they have and found these data 6 8 lo 6 7 6864 377 2 888 5 5 10 9 67 66 10 6 8 8 6 S 8 6 7 6 8 S 1 Designing the Distribution tables 2 2 11 9 4 3 13 9 4 6 8 6 6 76 9 10 88 9 6 7 9 7 6 4 3 8 2 7 S 7 3 3 2 6 6 7 6 6 73728 7 S 6 7 6 7 7 11 7 5778 8576 8 S S 3 tral moment Showing several types of aststitical charts Bar charts Histogram pie chartsiek 3 Calculating the teststitical averages Mean Median Mode Range Variance and SD 4 calculating probabilities CDF and PDF MPF

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ProbabilityProblem 4 2 pts How many seven card subsets of the set of 52 cards of the usual deck containing four aces four kings four queens etc contain simultaneously at least two aces at least two kings and at least one queen

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ProbabilityThe following circuit operates if and only if there is a path of functional devices from left to right The probability that each device functions is as shown Assume that the probability that a device is functional does not depend on whether or not other devices are functional What is the probability that the circuit operates 0 9 0 95 0 9 0 95 0 8 0 9

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ProbabilityThe following table gives amount of annual spending of a country s defense budget in billions of dollars for military construction Let x 12 correspond to the year 2012 Sketch the graph of the information in the table Year 2012 2013 2014 2015 2016 Spending 11 8 7 8 8 3 5 4 6 9 Choose an appropriate window for the graph The first value on the x axis should be 12 and the last value on the x axis should be 16 Since the maximum y value in the table is 11 8 the y axis will need to go as high as 12 Sketch the graph Choose the correct answer below OA 12 12 Year 16 Q OB 12 0 12 Year 16 O C 12 0 12 Year 16 Q OD 12 12 Year 16 Q

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ProbabilitySuppose your vehicle is licensed in a state that issues license plates that consist of three digits between 0 and 9 followed by three letters between A and Z If a license number is selected randomly what is the probability that yours is the one selected

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Probability2 You are interested in researching whether or not AP biology students who use a test prep book perform better on the exam than those who do not use a test prep book You take 60 random students and give 30 of them a test prep book while the other 30 will use the resources they already have After the students take the exam you analyze the data and find that of the students who used a test prep book 26 passed For the students who used only the resources they already had you found that 12 passed With this data would you suggest to future students to use a test prep book Step 1 state the null hypothesis There is no result difference between students who used the resources test prep book and those who didn t Step 2 determine your expected values Step 3 complete the Chi square chart Step 4 calculate your degrees of freedom Step 5 interpret results Purple flowers 543 White flowers 213 Does this data fit the predicted phenotypic ratios Step 1 state the null hypothesis Step 2 determine your expected values hint what should the phenotypic ratio be Step 3 complete the Chi square chart 3 In pea plants purple flowers P are dominant to white flowers p A plant that is heterozygous is self crossed The following phenotypes were observed Step 4 calculate your degrees of freedom Observed O Step 5 interpret results Expected E O E O E O E E Observed O Expected E O E Total O E O E E Total

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ProbabilityThe distribution of time community college students drive to campus is right skewed I recorded the mean and median travel time for my students Unfortunately I forgot to label them The numbers I wrote down are 21 minutes and 37 minutes Which number would be the mean 21 minutes 37 minutes

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ProbabilityOne year ago schools and businesses were shuttered to protect local communities from COVID 19 Below is the data from March 2020 March 21 2021 use this data to compare the risk of death for each local community Died Column Totals Survived 2 842 Norco 34 Community Observed Counts Riverside 806 53 212 V Eastvale Row Totals 84 1 Does this study suggest that community is associated with an increases the risk of death Select Be sure to identify the explanatory 8 329 and response Select 2 What is the relative risk of death for those that live in Norco Select variables use Riverside County s risk 0 014 as the basis for your comparison 3 What is the relative risk of death for those that live in Riverside Select use Eastvale as the basis for your comparison 4 Interpret the relative risk of death for those that live in Riverside compared to Eastvale

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ProbabilityHere are the data on the age of students that attend Norco College Age 19 and under 20 24 25 29 30 34 35 5 042 5 501 1 986 1 070 1 681 What is the probability of a student s age under 19 years old Round answer to 2 decimal places

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ProbabilityA researcher conducts an experiment to examine the differences in college costs in Illinois and New York Using StatCrunch dataset State College Costs compare and college costs between the Illinois and New York Choose all that apply NY has a smaller std dev than IL The median is about the same for NY and IL The range is larger for NY than IL The mean would be the appropriate measure of center The mean is larger for IL than NY The shape of the distributions are both symmetric

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ProbabilityAn article in the June 10 2002 issue of the Archives of Internal Medicine reported on a study of the effectiveness of nicotine lozenges to quit smoking Smokers who participated in the study were randomly assigned to receive either the nicotine lozenge being tested or a placebo no active ingredients lozenge Several variables were recorded on each subject including weight gender number of cigarettes smoked per day and whether or not the person had made previous attempts to quit smoking At the end of the study the primary variable recorded was whether or not the subject had successfully refrained from smoking Place a check next to each item that was a variable measured in this study O Whether the placebo helps reduce smoking Whether or not the subject had the lozenge or the placebo O Whether the lozenge helps reduce smoking Whether the person had previously attempted to quit smoking O Whether the subject had successfully refrained from smoking The smokers O Gender

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ProbabilityReese s Pieces candies and asked to record the color of each candy a What are the observational units Reese s Pieces Candy b What is the variable Select c Is it categorical also binary or quantitative Select Now suppose that your classmates are each given a sample of 25 Reese s Pieces candies Also suppose that students are asked to report the proportion of orange candies in their sample of 25 candies d Now what are the observational units Select e Now what is the variable Select

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ProbabilityUsing the Class Seating vs Grade data set in the Math 12 group in StatCrunch E create a graph and determine if females have a significantly higher GPA than males Choose the MOST correct statement from the following OYes the median GPA for females is 3 25 which is significantly higher than the median GPA of 3 0 for males O Yes the mean GPA for females is 3 24 which is significantly higher than the mean GPA of 2 95 for males O No the typical interval for females is 2 72 3 76 which is not significantly higher than the typical interval of males 2 33 3 57 O No the typical interval for females is 2 2 4 28 which is not significantly higher than the typical interval of males 1 71 4 19

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ProbabilityThe mean height for females is 64 inches with a standard deviation of 2 inches What is the shortest height that is still considered normal

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ProbabilityDuring the last presidential election CNN conducted an exit poll in which specific polling stations were randomly selected and all voters were surveyed as they left the premises Identify the sampling method used O Stratified Sample O Convenience Sample O Systematic Sample Cluster Sample

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ProbabilityThe mean height for females is 64 inches with a standard deviation of 2 inches What is the probability of one randomly selected female having a height between 60 inches and 68 inches Round answer to 2 decimals

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ProbabilityObservational studies are designed to be able to determine cause and effect True or False O True False

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ProbabilityWhich of the following is an example of a census O Survey students about the college class schedule by randomly selecting 500 from the college s enrollment records O To determine the median income of all working U S adults a marketing firm conducts a national survey of 50 000 randomly selected individuals across all 50 states A large retailer wants to determine the proportion of its customers who browse for merchandise online but make the final purchase in person at a store At the time of purchase each cashier is required to ask the customer whether the customer shopped online for the merchandise first O To determine the proportion of the graduating class that is college ready a local high school tests the reading comprehension of each 12th grader

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ProbabilityGiven the graph of the normal curve shown below what is the mean standard deviation f x 0 081 0 06 0 04 0 02 10 15 ta 8 30 35 140 and

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ProbabilityHere is a passage from a study published by the National Highway Traffic Safety Administration in 2007 The National Occupant Protection Use Survey NOPUS is the only probability based survey of driver cell phone use in the United States The survey observes usage as it actually occurs at a random selection of roadway sites and so provides the best tracking of the extent to which people in this country are using cell phones while driving NOPUS observed 43 000 drivers in this study Identify the population and sample in the study O Population 43 000 Drivers in this study Sample Drivers at the randomly selected roadway sites O Population Drivers in the United States Sample 43 000 Drivers at randomly selected roadway sites O Population U S drivers Sample 43 000 Drivers at randomly selected roadway sites O Population U S drivers Sample 43 000 drivers using their cell phones

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ProbabilityThe incubation period for the eggs of a House Wren has a normal probability distribution with a mean time of 336 hours and a standard deviation of 3 5 hours Before hatching a particular House Wren egg incubated for 346 hours What is the probability that House Wren eggs will take longer than 346 hours to hatch Round to 3 decimal places

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ProbabilityBased on the table what is the probability that a coin toss ends up with a head Round to 1 decimal place P H Frequency distribution for a coin toss Tail Outcome Head Number of tosses with each 60 outcome 140

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ProbabilitySolve each of the following equations for x Equation x 8 17 5x 8 23 185x 42 Solution x 9 x 3 x 12 Organize each of the following equa Qas a function of P Q 15 P Q 25 5P 60 18 3P P as a f P 15 e P Q 15 P 15 Q P 15 Q ss P as a function of Q

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ProbabilityStudents want to investigate this question Is there a relationship between the number of hours high school students spend each week on Facebook and their high school GPA grade point average Which study design is most appropriate O Divide high school students into two groups Flip a coin to decide who is in each group One group goes onto Facebook for 5 minutes then takes a short quiz The other group just takes the short quiz O Go to a local high school and survey students during their study hall period In the survey ask students to estimate the hours they spend on Facebook each week Obtain the GPA data for these students from the high school counselor O Send out a survey to your friends on Facebook Ask them to take the survey and to forward it to their Facebook friends In the survey ask two questions How many hours do you spend on Facebook each week What was your GPA in high school Collect at least 100 responses

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ProbabilityThe following list gives the home run totals for Barry Bonds from 1986 through 2007 his total career 0 1 2 Next question 3 4 16 25 24 40 23 37 34 You can retry this question Construct a stem and leaf plot for the data Enter the leaves in ascending order without spaces between them If a stem has no corresponding leaves leave that space blank Stems Leaves 5 19 33 49 73 34 46 25 45 45 46 37 5 33 42 26 28

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ProbabilityAnouk and Tessa are playing a game where a player flips a coin If the coin lands on heads the player receives 1 point If the coin lands on tails the player receives 2 points The expected value of a turn is 1 5 points Which of the following statements are true Choose all answers that apply A B C The total number of points from 2 turns must be exactly 3 points It is possible for a player to get 1 5 points on a turn If they play a large number of turns they should expect to average about 1 5 points per turn

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ProbabilityDetermine whether the following is a probability distribution or not X P x 0 0 243 1 0 167 2 0 213 3 0 149 4 0 232 5 0 164 Select one True False

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ProbabilitySuppose a certain magazine evaluates products for consumers The following table contains data for 15 compact sports utility vehicles SUVS from a certain year Vehicle name of vehicle Overall score awarded based on a variety of measures including those in this data set Recommended Consumer Reports recommends the vehicle or not Owner satisfaction satisfaction on a five point scale based on the percentage of owners who would purchase the vehicle again 0 Overall miles per gallon miles per gallon achieved in a 150 mile test trip Acceleration 0 60 sec time in seconds it takes vehicle to reach 60 miles per hour from a standstill with the engine idling Vehicle SUV 1 SUV 2 SUV 3 SUV 4 SUV 5 SUV 6 SUV 7 SUV 8 SUV 9 SUV 10 SUV 11 SUV 12 SUV 13 SUV 14 SUV 15 Overall Score 82 81 79 71 69 69 67 65 63 61 61 55 55 53 48 Recommended Yes Yes Owner Satisfaction Querall Milos Per Gallon Yes Yes Yes Yes Yes No No No No No No No No a How many variables are in the data set 6 x Owner Satisfaction 0 0 0 0 0 0 b Which of the variables are categorical Select all that apply Overall Score Recommended Overall Miles Per Gallon 27 28 25 25 25 24 24 22 26 25 32 27 23 23 25 Acceleration 0 60 Sec 8 9 8 8 9 5 9 7 8 8 9 8 10 3 8 7 10 5 10 2 10 3 8 6 7 4 10 9 10

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ProbabilityThe following data show the number of rental cars in service for three rental car companies Hertz Avis and Dollar over a three year period t Cars in Service 1000s Company Year 1 Cars in Service 1000s Hertz Cars in Service 1000s Dollar Avis 300 250 200 150 100 50 0 350 300 250 200 150 100 a Construct a time series graph for the years 1 to 4 showing the number of rental cars in service for each company Show the time series for all three companies on the same graph 350r 350r 350r 50 0 Year 1 327 Year 1 167 204 Year 2 311 140 220 Dollar Avis Hertz Year 2 Hertz Avis Dollar Year 2 Year 3 Year 286 106 300 Year 3 Year 4 Year 3 290 108 270 Year 4 Year 4 5 300 250 200 150 100 50 0 Year 1 Year 2 Year Avis Dollar Hertz Year 3 Year 4 DO 300 250 200 150 100 50 0 Year 1 Year 2 Year Dollar Hertz Avis Year 3 Year 4

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ProbabilityWhat does it mean for the findings of a statistical analysis of data to be statistically significant Choose the correct answer below O A The outcome could easily occur by chance B The results are very important to the health and well being of a certain population C The results do not make enough difference to be of use D The likelihood of getting these results by chance is very small

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ProbabilityWhich of the following is NOT a voluntary response sample Choose the correct answer below OA A survey is taken at a mall by asking passersby if they will fill out the survey OB A radio station asks for call in responses to a question concerning city recycling C A local dentist asks her patients to fill out a questionnaire and mail it back to determine the quality of the care received during an offic O D Quiz scores from a college level statistics course are analyzed to determine student progress

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ProbabilityAn editorial criticized a chart caption that described a dental floss as one that reduces the chance of plaque on teeth by over 250 percent What is wrong with this statement Choose the correct answer below KERID O A A reduction of 100 would eliminate all plaque so it is not possible to reduce it by more than 100 O B plaque fell by 100 it would be cut in half Thus a decrease of 200 means that it would be totally eliminated and a decrease of more than 200 is impossible OC The actual amount of the decrease in plaque is less than 100 OD The statement does not mention the initial amount of plaque

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ProbabilityRefer to the table of body temperatures degrees Fahrenheit Is there some meaningful way in which each body temperature recorded at 8 AM is matched with the 12 AM temperature Subject 3 1 2 5 4 8 AM 97 0 98 5 97 6 97 7 98 7 12 AM 97 6 97 8 98 0 98 4 98 4 Choose the correct answer below COD OA Yes The 8 AM temperatures are all from one individual over five days and the 12 AM temperatures are from a different individual on the same five days so each pair is matched OB No The 8 AM temperatures are from one individual over five days and the 12 AM temperatures are from another individual over five days O C Yes Each column of 8 AM and 12 AM temperatures is recorded from the same subject so each pair is matched D Yes The 8 AM temperatures are all from one individual over five days and the 12 AM temperatures are from the same individual on the same five days so each pair is matched

Statistics

Probabilitycorrectness of your methods as well as on the An administrator at a large university wants to conduct a survey to estimate the proportion of students who are satisfied with the appearance of the university buildings and grounds The administrator is considering three methods of obtaining a sample of 500 students from the 70 000 students at the university a Because of financial constraints the first method the administrator is considering consists of taking a convenience sample to keep the expenses low A very large number of students will attend the first football game of the season and the first 500 students who enter the football stadium could be used as a sample Why might such a sampling method be biased in producing an estimate of the proportion of students who are satisfied with the appearance of the buildings and grounds b Because of the large number of students at the university the second method the administrator is considering consists of using a computer with a random number generator to select a simple random sample of 500 students from a list of 70 000 student names Describe how to implement such a method c Because stratification can often provide a more precise estimate than a simple random sample the third method the administrator is considering consists of selecting a stratified random sample of 500 students The university has two campuses with male and female students at each campus Under what circumstance s would stratification by campus provide a more precise estimate of the proportion of students who are satisfied with the appearance of the university buildings and grounds than stratification by gender

Statistics

Probability1 For each day that Sasha travels to work the probability that she will experience a delay due to traffic is 0 2 Each day can be considered independent of the other days a For the next 21 days that Sasha travels to work what is the probability that Sasha will experience a delay due to traffic on at least 3 of the days b What is the probability that Sasha s first delay due to traffic will occur after the fifth day of travel to work c Consider a random sample of 21 days that Sasha will travel to work For the proportion of those days that she will experience a delay due to traffic is the sampling distribution of the sample proportion approximately normal Justify your answer

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ProbabilityP A B Probability of A occurring given that B has already occurred given in a pr blem Problem T event of selecting a tall man H event of selecting a high income earner a What is n T b How many elements are in the universe c What does P T mean d What is P T e What does P T H mean f What is P T H The decimals may be rounded to three decimal places if needed a n T T TT VE 22 101 21 is 48 H

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Probabilitycigarettes bad peopler Cigar smoki are definitely not good for a person s health and the last ingredient can cause addiction stem 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Brand 18 Brand A 14 2 Brand B Brand D Brand C 29 7 Brand E Brand F Brand G Brand H Brand I Brand J Brand K Brand L Tar Nicotine co Brand M 15 9 leaf 8 1 4 2 15 1 8 7 12 5 16 5 14 8 13 8 15 0 7 9 0 76 13 5 Brand N 1 26 2 23 16 7 23 4 1 24 14 9 0 86 9 1 1 05 12 4 1 02 16 2 0 91 0 92 15 5 0 77 10 3 Brand Q 17 2 0 40 5 3 Brand R 13 1 Brand Tar Nicotine Co Brand O 0 47 10 1 Brand P Brand S Brand T Brand U Brand V Brand W Brand X 1 00 14 3 Brand Y 11 3 9 2 1 2 12 7 15 9 4 4 14 4 7 2 8 7 oxide and nicotine measured in milligrams The first to 15 3 Use the data in the table above to make a stem and leaf display for milligrams of carbon monoxide per cigarette smoked Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values 12 1 0 68 10 1 0 64 9 4 0 13 1 36 18 6 1 18 1 4 0 22 0 76 17 6 12 5 0 51 4 9 1 11 15 8 8 6 0 59 10 7 1 02 14 0 0 72 15 0