Statistics Questions

X is a discrete random variable The table below defines a probability distribution for X What is the expected value of X HO3T9 0 7 10 P X x 0 3 0 5 0 1 0 1 Show Calculator

is a discrete random variable The graph below defines a probability stribution for X What is the expected value of X P X 2 0 5 0 45 0 4 0 35 0 3 0 25 0 2 0 15 0 1 0 05 0 50 25 25 50

How is a sample related to a population Choose the correct answer below OA A sample is a subset of a population OB A sample is the collection of all outcomes responses measurements or counts OC A sample is a numerical measure that describes a sample characteristic

How does the Part 2 A different car s value is represented by the equation y 45 000 3 3 Explain what the numbers 45 000 and represent in this situation a b After how many years will the car s value be less than half its original value

Determine 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

on 0 60 Sec ariables are quantitative Select all that apply core ended atisfaction Miles Per Gallon tion 0 60 Sec tage of these 15 vehicles are recommended Round your answer to the nearest percent average of the overall miles per gallon across all 15 vehicles Round your answer to one decimal place miles per gallon atisfaction construct a bar chart showing the percentage frequency for each of the owner satisfaction ratings 50 50 45 45 40 40 35 30 25 20 15 10 0 Owner Satisfaction 44 6 Percentage Frequency 5 70 79 80 89 9 0 9 9 10 0 10 9 Acceleration 0 60 Sec Frequency 6 5 0 Owner Satisfaction 2 44 Percentage Frequency 35 30 25 20 15 10 7 0 7 9 8 0 8 9 9 0 9 9 10 0 10 9 Acceleration 0 60 Sec 0 Owner Satisfaction frequency distribution for acceleration using the following intervals 7 0 7 9 8 0 8 9 9 0 9 9 and 10 0 10 9 Construct a histogram showing the frequencies of each interval 3 Frequency 6 5 Percentage Frequency 7 0 7 9 50 45 40 35 30 25 20 15 10 0 Owner Satisfaction 8 0 8 9 9 0 9 9 10 0 10 9 Acceleration 0 60 Sec 4 6 5 1 7 0 7 9 8 0 8 9 Acceleration 0 60 Sec 9 0 9 9 10 0 10

he sales revenue for a footwear company over a four year period are as follows Year 1 2 3 4 Sales in Billions PN W AU Sales Billion Net Income 5 billions 2 21 Use this information to answer the following questions a Are these cross sectional or time series data 6 3 25 These are cross sectional data because the data were collected over time These are cross sectional data because the data were collected all at once These are time series data because the data were collected all at once These are time series data because the data were collected over time 3 66 b Construct a bar graph similar to the given figure 4 06 1 0 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Year Net Income for McDonald s Inc 2 Year 3 4 DO Sales nic 1 2 Year 3 4 Sales in Billions NW 44 2 Year 3 4 Sales in Billions L 1 2 Year 3 4

Suppose 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

Model name of the model 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 Make Subaru Honda Toyota Nissan Mazda Kia Ford Mitsubishi Hyundai GMC Jeep Model Forester Jeep CRV Rav4 Rogue CX 5 Sportage Chevrolet Equinox Escape Outlander Volkswagen Tiguan Limited 67 Volkswagen Tiguan Tucson Terrain Cherokee Compass Overall Score a How many variables are in the data set Owner Satisfaction 84 83 81 73 71 71 69 65 63 63 57 57 55 50 Recommended Yes Yes Yes Yes Yes Yes Yes No No No No No No No No b Which of the variables are categorical Select all that apply Overall Score Recommended Owner Satisfaction 0 0 0 0 0 0 0 Overall Miles Per Gallon 26 27 24 24 24 23 23 21 25 24 31 26 22 22 24 Acceleration 0 60 Sec 8 7 8 6 9 3 9 5 8 6 9 6 10 1 8 5 10 3 10 0 10 1 8 4 7 2 10 9 9 8

snown Product Information for 10 Tablet Computers Cost Operating System Tablet Acer Iconia W510 Amazon Kindle Fire HD Apple iPad 4 HP Envy X2 Lenovo ThinkPad Tablet Microsoft Surface Pro Motorola Droid XYboard Samsung Ativ Smart PC Samsung Galaxy Tab Sony Tablet S 599 299 cost 499 860 cost operating system display size battery life cpu manuafacturer 668 899 530 590 525 a How many elements are in this data set 10 360 b How many variables are in this data set 4 Windows Android IOS Windows Windows Windows Android Windows Android Android c Which variables are categorical Select all that apply Display Size inches operating system display size battery life cpu manuafacturer Which variables are quantitative Select all that apply d What type of measurement scale is used for cost nominal scale 10 1 8 9 9 7 11 6 10 1 10 6 10 1 11 6 10 1 9 4 ordinal scale interval scale ratio scale What type of measurement scale is used for operating system Battery Life hours 8 5 9 11 8 10 5 9 7 10 8 CPU Manufacturer Intel TI OMAP Apple Intel Intel Intel TI OMAP Intel Nvidia Nvidia

A Bloomberg Businessweek North American subscriber study collected data from a sample of 2 861 subscribers Fifty nine percent of the respondents indicated an annual income of 75 000 or more and 50 reported having an American Express credit card a What is the population of interest in this study the percentage of subscribers of Businessweek in North America who have an American Express card the percentage of subscribers of Businessweek in North America who have an annual income of 75 000 or more the 50 of respondents who reported having an American Express card all subscribers of Businessweek who participated in the survey all subscribers of Businessweek in North America at the time the survey was conducted b Is annual income a categorical or quantitative variable categorical quantitative c Is ownership of an American Express card a categorical or quantitative variable categorical Oquantitative d Does this study involve cross sectional or time series data cross sectional time series e Describe any statistical inferences Bloomberg Businessweek might make on the basis of the survey Using the sample results we could infer or estimate 59 of the population of subscribers have an Select

Tablet Acer Iconia W510 Amazon Kindle Fire HD Apple iPad 4 HP Envy XZ Lenovo ThinkPad Tablet Microsoft Surface Pro Motorola Droid XYboard Samsung Ativ Smart PC Samsung Galaxy Tab Sony Tablet S Cost Operating System 599 299 499 860 668 899 530 590 525 What is the average cost for the tablets 360 Windows Android IOS Windows Windows Windows Android Windows Android Android Display Size Battery Life inches hours 10 1 8 9 9 7 11 6 10 1 10 6 10 1 11 6 10 1 9 4 What percentage of tablets use a CPU manufactured by Nvidia What percentage of tablets use an Windows operating system 8 5 9 11 8 10 5 4 9 7 10 8 Manufacturer Intel TI OMAP Apple Intel Intel Intel TI OMAP Compare the average cost of tablets with a Windows operating system to the average cost of tablets with an Android operating system The average cost of a tablet with a Windows operating system is android operating system on average Intel Nvidia Nvidia The average cost of a tablet with an Android operating system is Thus we see tablets with Windows operating systems co Select than table less than more than H

The 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

Determine whether the data described below are qualitative or quantitative and explain why The numbers of cases of flu treated at a certain hospital in different years Choose the correct answer below OA The data are qualitative because they don t measure or count anything OB The data are qualitative because they consist of counts or measurements O C The data are quantitative because they don t measure or count anything OD The data are quantitative because they consist of counts or measurements

Determine whether the underlined number is a statistic or a parameter A sample of professors is selected and it is found that 25 own a computer m Choose the correct statement below Parameter because the value is a numerical measurement describing a characteristic of a samp O Statistic because the value is a numerical measurement describing a characteristic of a sample Parameter because the value is a numerical measurement describing a characteristic of a popul O Statistic because the value is a numerical measurement describing a characteristic of a populati

Use the Statistical and Critical Thinking flow chart interactive to answer the following ques Which one of the following is a correct statement Choose the correct answer below A If results from a statistical study are likely to occur by chance then the study has statistical significance B If a statistical study has statistical significance then it must also have practical significance OC A statistical study could have statistical significance but not practical significance OD If results from a statistical study are rpt likely to occur by chance then the study has practical significance

Use the Statistical and Critical Thinking flow chart interactive to answer the following question In a statistical study 500 adult patients were treated for high blood pressure and 495 of them had lower blood pressure after the treatment Which one of the following is a correct statement Choose the correct answer below KER OA The study has statistical significance because it is important to lower blood pressure in adults OB The study has statistical significance because the results are extremely unlikely to occur by chance OC The study does not have statistical significance because some of the treated patients did not have lower blood pressure OD The study has statistical significance because the sample size of 500 is large

What 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

Which 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

An 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

b Could the result from part a be the actual number of survey subjects who said that their companies conduct criminal background checks on all job applicants Why or why not OA No the result from part a could not be the actual number of survey subjects who said this because that is a very rare outcome O B No the result from part a could not be the actual number of survey subjects who said this because a count of people must result in a whole number OC Yes e result from part a could be the actual number of survey subjects who said this because the polling numbers are accurate O D Yes the result from part a could be the actual number of survey subjects who said this because the result is statistically significant

In a study conducted by a human resource management organization 483 human resource professionals were surveyed Of those surveyed 67 said that their companies conduct criminal background checks on all job applicants Complete parts a through d a What is the exact value that is 67 of 483 survey subjects The exact value is Type an integer or a decimal Do not round CLOOB

A A magazine ran a survey about a web site for downloading music Readers could register their responses on the magazine s web site Identify what is wrong Choose the correct answer below OA It is likely that the survey used a loaded question so the results of the survey are not reliable OB The sample is a census so there is a good chance that the results do not reflect the population OC The magazine has an interest in the survey results so the source of the survey is questionable O D The sample is a voluntary response sample so there is a good chance that the results do not reflect the population

Several studies showed that after eating a very large meal subjects had increased risk of heart attack A diet food manufacturer financed this research Identily What wrong Choose the correct answer below COLOD OA It is not possible to take accurate measurements OB The data used in the studies is not reliable because it was not measured by the administrator OC It is questionable that the sponsor is a diet food manufacturer because this sponsor can be greatly affected by the conclusion OD Since the research is composed of voluntary response samples there may be key data points missing

Refer 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

REBECCA S BALANCE Rebecca carries a balance on her credit card each month Today is the first day of the new 28 day billing cycle The current balance is x and the APR is 24 Rebecca is buying a friend an expensive gift that costs 1 400 that she plans to put on her credit card This will be her only purchase this month and she will be making this purchase on the last day of the month Part A If her finance charge will be 51 write and solve an equation to determine her current balance on her credit card Show your work Part B How much in finance charges can she save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle Explain how you determined your answer

9 Market equilibrium and disequilibrium The following graph shows the monthly demand and supply curves in the market for calendars Use the graph input tool to help you answer the following questions Enter an amount into the Price field to see the quantity demanded and quantity supplied at that price You will not be graded on any changes you make to this graph PRICE Dollars per calendar 100 88323922 00 Supply Demand 50 100 150 200 250 300 350 400 450 000 QUANTITY Calendars The equilibrium price in this market is s Graph Input Tool Price Dollars per calendar Shortage or Surplus 40 60 Market for Calendars 1 price 40 shortage or surplus 2 price 60 shortage or surplus Price Dollars per calendar Quantity Demanded Calendars per calendar and the equilibrium quantity is 30 500 Shortage or Surplus Amount Calendars Quantity Supplied Calendars Complete the following table by indicating at each price whether there is a shortage or surplus in the market the amount of that shortage or surple and whether this places upward or downward pressure on prices 210 Pressure calendars bought and sold per month

PRICE Thousands of dollars per sedan 8 30 20 curve Demand for Sedans Demand 100 200 300 400 500 600 700 800 900 QUANTITY Sedans per month are An increase in average income causes a rightward are Demand for Sedans Price of a sedan Thousands of dollars Quantity Demanded Sedans per month Demand Shifters Average Income Thousands of dollars 1 movement along or shift of 2 shift of or movement along 3 a normal or an inferior 4 substitutes or complements Price of Gas Dollars per gallon Price of a Subway Ride Dollars 20 450 Consider the graph Suppose that the price of a sedan increased from 15 000 to 20 000 This would cause a 50 4 2 the demand curve therefore you may conclude that sedans good Hint Try substituting different values for Average Income in the calculator and observing what happens Suppose that due to an increase in the supply of gasoline the price of a gallon of gas falls from 4 to 3 Because sedans and gasoline decrease in the price of a gallon of gas shifts the demand curve for sedans to the the demand

a h Determine the maximum normal stress or in the beams shown here using the values as needed L 2 m a 0 5 mw 12 KN m P 25 KN Assume a rectangular cross section of width b 20 cm and height h 30 cm es VOORGES AFEXUBE a L 2 1 1 FANA KIEMERG 5 d L I 20 I 30 bh3 12 2030 12

assifying Data by Level In Exercises 13 18 determine whethe e qualitative or quantitative and identify the data set s level of mea plain your reasoning Football The top five teams in the final college football poll re January 2007 are listed Source Associated Press 1 Florida 2 Ohio State 3 LSU 4 USC 5 Boise State

14 For the cantilever beam and loading shown determine the slope and deflection at point C EI 1 A 15 KN B 11 KN C

the deflection of the loading point the point al direction of the load for the trusses given below All elements are constructed of 20 mm diameter round carbon steel rods the s 0 6 m 1 m 25 km 2 5 kN 3 N 0 4 m 1 0 7 m 1 m 1 2 m 2 kN 2 kN

8 Calculate the value of the modulus of elasticiy and the Poisson ratio for the following member y L 1200 mm 8 300 m X d 22 mm 6 2 4 m 25 kN X

An investor is going to purchase one of three types of real estate The investor must decide among an apartment building an office building and a warehouse The future states of nature that will determine how much profit the investor will make are good economic conditions and poor economic conditions The profits in thousands that will result from each decision in the event of each state of nature are shown in the following table Decision Purchase Apartment building Office building Warehouse Decision Purchase a Construct Opportunity Loss Regret Table Apartment building Office building Warehouse Good Economic Conditions 550 1030 385 States of Nature States of Nature Good Economic Conditions Poor Economic Conditions 340 370 105 Poor Economic Conditions b Determine the best decision using the Opportunity Loss decision criterion O Decision Apartment building based on 480 min 480 710 645 O Decision Warehouse based on min 235 except zeros O Decision Office building based 710 max 480 710 645 O Decision Warehouse based on 880 max 480 710 880

correctness 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

1 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

P 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

A job in an insurance office involves telephone conversations with policyholders The office manager estimates that about half of the employee s time is spent on the telephone How many observations are needed in a work sampling study to estimate that time percentage to within 6 percent and have a confidence of 95 0 percent Round z values to 2 decimal places Do not round other intermediate calculations Round your final answer to the nearest whole number Number of the

cigarettes 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

The figure below shows the residual plot for a data set Residuals 6 3 3 6 2 4 6 8 10 Which statement is true O A A random pattern of the residual plot supports a linear model OB A random pattern of the residual plot supports a nonlinear model OC The data set is linear because the sum of the residuals is greater than zero O D The data set is nonlinear because the sum of the residuals is greater than zero

Let s practice more examples Decide if each statement is true or false and then exp your reasoning Expression 5 3 12 8i 6i is equivalent to 9 2i Subtract distribute the negative 6 51 15 9i 1 is equivalent to 10 8i 7 1 121 3 bi 2 7i b 5 would make the equation true 8 i 1 3 31 271 Select One True False True False True False True False True False I think so because 3 12 Y 161 9 21

Justified True or False with Complex Numbers 11 Write each expression in the form a bi where a and b are real numbers Justify your solution by drawing a diagram Expression 1 3 1 1 21 4 1 311 1 21 4 1 2 5 1 6 3i 1 2i 5 i 6 31 1 41 3 5 31 1 4i 4 i 5 31 1 41 41 4 4 2i 6 3i 2 5i 4 21 6 31 2 5 Select One True False True False True False True False Prove or disprove by using a visual diagram 20 20 11 12 11

Student s ID 1 Please show the records for transactions mentioned below for the first month of 2023 Please remember the company you chose to study during the semester and make all transactions for the year 2023 for the mentioned company a Write basic equation for the year 2022 for your company b Borrowed TL4 500 000 from the bank with signing a note payable in the name of the business c Paid cash of TL2 000 000 to a real estate company to acquire land d Performed service for a customer and received cash of TL1 000 000 e Purchased supplies on credit TL300 000 f Performed customer service and earned revenue on account TL260 000 g Paid TL120 000 on account h Paid the following cash expenses salaries TL3 000 000 rent TL15 000 and interest TL4 000 i Received TL310 000 on account j Received a TL20 000 utility bill that will be paid next week k Declared and paid dividends of TL1 800 000 1 Rewrite basic equation for January 31 2023 for your company

2 Name Ava Hodgson 1 Which of the following represents a self selective sampling each person in the sample is numbered and the sample is obtained by selecting every third number B people are invited to participate in a survey and in some cases are rewarded for their participation a set number of people each of whom have an equal chance of being selected are chosen at random from an entire population D individuals who share a common location or characteristic are selected to respond To determine which ten favorite songs should be played at a school dance the student council should A ask the school principal 3 A b time the belc all min

Yea r 0 1 2 3 4 5 7 Eleven RM 35 000 12 500 10 000 8 500 5 000 8 000 Speedmart RM 35 000 8 000 8 000 8 000 8 000 8 000

polling booth Sprobability that is the muld be askied before you can find of people eatiting from and asking drom If they voted independently In a Suney them 6 that a person reted independently is 00 probability that is people must Speople who voted independent from a polling The

Your friend offers the following wager you roll a fair die If a four comes up he will pay you 11 but if any other number comes up you will have to pay him 2 What is the expected value of this game

888 A pair of dice are rolled a How many total outcomes are possible b List the set of outcomes that make up the event a sum of nine rolled c What is the probability of a sum of nine being rolled

I am going to the beach and want to take some books to read From the 12 books on my shelf I grab 8 How many different ways can I choose the books to take with me

You have a password which is made up of 6 letters What is the probability that there are no letters repeated