Statistics Questions

from the set 3 4 5 82 Which event by definition covers the entire sample space of this experiment Choose Choose The number is neither prime nor composite Please answer all parts of the questi The square root of the number is less than 3 The number is divisible by 3 1 and loss than 99

What is the sample space for the following spinner Blue Green Red Select one O a 4 Red Yellow Blue O b Red Red Yellow Green Blue Blue O c Yellow Green Blue O d Red Yellow Green Blue

Jim 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

What 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

Alexis works at a health care facility She has measured the hemoglobin levels of 400 people The data follows a normal distribution with a mean of 16 g dL and a standard deviation of 2 What is the chance that if Alexis pulls a file randomly that that patient would have a hemoglobin level between 12 and 20 g dL Select one a 20 O b 50 c 99 7 O d 95 e 68

You have 5 different colored boxes In how many distinct ways can the boxes be ordered Select one O a 120 O b 5040 O c 365 O d 720

If 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

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

The 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

Hae Won records her checking account activity in dollars for one month Her withdrawals and deposits are shown in the table Date 2021 06 01 2021 06 01 2021 06 05 2021 06 09 2021 06 15 2021 06 18 2021 06 20 2021 06 21 2021 06 25 2021 06 30 Description Previous Balance Check 1001 Mortgage Check 1002 Car Payment ATM no fee Paycheck Check 1003 Groceries Transfer to savings ATM no fee ATM no fee Paycheck Withdrawals O A 1 850 22 d 1 989 10 1 240 00 315 50 175 29 1 500 00 230 00 B 1 850 22 3 460 79 d 1 989 10 Deposits OC 1 850 22 3 599 67 d 1 989 10 175 00 1 537 33 350 00 1 537 34 Which equation could be used to determine the total amount d in dollars of the deposits for this month in Hae Won s account Balance 1 850 22 610 22 294 72 469 72 2 007 05 1 831 76 331 76 681 76 451 76 1 989 10

You may use a calculator for this item The day Daniela starts a new job she opens a checking account into which she deposits 2 200 and a savings account into which she deposits 800 Each week Daniela is paid 1 200 which is directly deposited into her checking account Then 700 of that money is immediately transferred to her savings account The system of equations models this situation where y is an account balance in dollars 2 weeks since Daniela started working y 500x 2 200 y 700x 800 Without any other deposits or withdrawals after how many weeks will Daniela have the same amount of money in each account Enter your answer in the box

Fair wheel of chance experiment from 0 to 12 Ex x A

Which 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

graph ermine the equation of the y Use integers or fractions for any numbers in the expression 0

Translate each sentence using the following translation key Bob is gathering eggs Question 5 Cv D Question 6 B Bob has fed neither the chickens nor the ducks Question 7 C D Question 8 P Bob has fed the chickens Bob has fed the ducks Bob is gathering eggs and has fed the chickens and he has fed the ducks The ducks are playing in the pond If Bob hasn t fed the ducks then he has fed the chickens 2 points 2 points 2 points

Question 14 Question 15 B Question 16 C D Question 17 F P Q S Bob is gathering eggs Bob has fed the chickens Bob has fed the ducks Bob is chasing the fox The ducks are playing in the pond away It s not the case that both Bob is chasing the fox away and the chickens are playing in the pond 2 points The ducks are quacking loudly The chickens are playing in the pond Either Bob has fed the ducks and is chasing the fox away or he has fed the chickens Bob is chasing the fox away and he has either fed the chickens or they are playing in the pond If the ducks are playing in the pond then the chickens are playing in the pond only if Bob is chasing the fox away 2 points 2 points 2 points

Question 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

local 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

The owner of the Rwanda Computer Company must decide among building 100 servers building 5000 hard drives or leasing all their 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 The specialists calculated the likelihood for each possible level of material costs In the payoff table below the estimated profit losses are given in thousands Servers Hard Drives Leasing Probability of State of lature Decision EMV Hard Drives Select an answer V Stable 1830 1900 EVPI 550 e Please interpret EVPI 0 3 Material Costs Moderate Increase 1010 a Compute the expected monetary value for each decision EMV Servers c Find the expected value with perfect information EVWPI 500 900 EMV Leasing b Using Expected Monetary Value criterion select the best decision 0 4 d Determine the expected value of perfect information Significant Increase 170 2400 850 0 3 O EVPI is the average amount the company would pay for additional information O EVPI is the usual amount the company would pay for additional information O EVPI is the maximum amount the company would pay for additional information O EVPI is the minimum amount the company would pay for additional

cision 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

The owner of the Wynston Transport Company must decide among manufacturing 10 new transport trucks manufacturing 20 000 new electric scooters or leasing all their manufacturing 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 Stable 1800 1910 600 Material Costs Moderate Increase 350 820 1000 Transport ecision Scooters Leasing ermine the best decision using the Hurwicz criterion with a 0 2 O Decision Scooters based on 1438 max 940 1438 920 O Decision Transport based on 1640 min 1640 22 680 O Decision Leasing based on 680 max 1640 22 680 O Decision Stable based on 862 max 862 480 1860 Significant Increase 2500 450 700

The owner of the Gatesville Transport Company must decide among manufacturing 10 new transport trucks manufacturing 20 000 new electric scooters or leasing all their manufacturing 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 The specialists calculated the likelihood for each possible level of material costs In the payoff table below the estimated profit losses are given in thousands Transport Decision Scooters Leasing Probability of State of Nature Transport Decision Scooters a Construct Opportunity Loss Regret Table Leasing Probability of State of Nature Stable EOL Scooters 1810 2200 810 EOL Leasing 0 4 Stable 0 4 c Select the best decision using EOL criterion O Decision Scooters O Decision Leasing O Decision Transport Material Costs Moderate Increase 1020 650 920 b Compute the expected opportunity loss value for each decision EOL Transport d Which of the following formulae is correct 0 5 Material Costs Moderate Increase 0 5 Significant Increase 150 2350 1050 0 1 Significant Increase 0 1

A chicken soup recipe calls for 13 cups of chicken stock How much is this in quarts Write your answer as a whole number or a mixed number in simplest form J Conversion facts for volume 1 cup c 1 pint pt 2 cups c 1 quart qt 2 pints pt 8 fluid ounces fl o

Questions 3 6 Three students named Abe Barb and Cal make measurements in m of the length of a table Find the means on 1 a using the data given Student Abe Barb L 1 4717 1 4753 L2 1 4711 1 4759 L3 1 4722 1 4756 1 45 LA 1 4715 1 4749 1 4705 L On l 8

A 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

Suppose 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

The 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

Cycle time in manufacturing can be viewed as the total time it takes to complete a product from the beginning of the production process The concept of cycle time varies according to the industry and product or service being offered Suppose a boat manufacturing company wants to estimate the mean cycle time it takes to produce a 16 foot skiff A random sample of such skiffs is taken and the cycle times in hours are recorded for each skiff in the sample The data are analyzed using Minitab and the results are shown below in hours What is the point estimate for cycle time How large was the sample size What is the level of confidence and what is the confidence interval What is the margin of error of the confidence interval One Sample T N Mean StDev SE Mean 26 25 41 5 34 98 CI 1 05 22 81 28 01

Determine the domain for g x 3x 5 5x 7 Interval notation please Upload a PDF of your work in the correct orientation Only PDFs will be given credit Show all work Give exact answers

b 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

In 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

A 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

Exhibit to answer question Bacon 50 40 30 20 10 A B E F C D 10 20 30 40 50 60 70 Eggs F represents a a combination of production that can be reached if we reduce the production of eggs by 20 units b a combination of production that is inefficient because there are unemployed resources c a combination of production that can be reached if there is a sufficient advance in technology d none of the above

se Exhibit to answer question Bacon 50 40 30 A 20 10 B E F C D 10 20 30 40 50 60 70 Eggs s we move from point A to point D O a the opportunity cost of eggs in terms of bacon is constant Ob the opportunity cost of eggs in terms of bacon rises Oc the opportunity cost of eggs in terms of bacon falls d the economy becomes less efficient Oe the economy becomes more efficient

52 m o 2 5 m 45 47 49 51 53 55 57 59 Braking distance in meters X 31 Find the braking distance of a Ford Expedition that corresponds z 2 4 32 Find the braking distance of a Ford Expedition that corresponds to z 1 2 33 What braking distance of a Ford Expedition represents the 95th percentile 34 What braking distance of a Ford Expedition represents the third quartile 35 What is the shortest braking distance of a Ford Expedition that can be in the top 10 of braking distances be in the

I 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

2 Calculate the median number of runs allowed in cloudy games 14 3 Cubs pitchers had two very bad days giving up 13 and 14 runs Calculate the mean and median without these two values How do these values affect the two measures of center Example 2 Once again using the Cubs runs allowed data for cloudy day games answer the following questions 0 4 11 6 2 4 4 3 6 6 3 10 4 4 9 13 13 1 Calculate the range of the data 3 4 9 3 6 5 3 3 2 Calculate and interpret the interquartile range IQR 1 3 If we eliminated the Cubs two bad days giving up 13 and 14 runs what is our new range and IQR How do these values and removing them from our list affect these two measures of variability

4 Describe the shape center and variability of the distribution Caution You cannot obtain complete shape information from a boxplot i e of peaks Example 3 The boxplots summarize the distributions of age for three types of U S skiers in the 2018 Winter Olympics Alpine skiing includes events such as downhill and slalom Cross county skiing includes events such as the 30K women s race 50K men s race and various relays Freestyle skiing includes events such as halfpipe and aerials Compare these distributions Cross country skiing Solution Shape Outliers Center Alpine skiing Freestyle skling Variability Overall 218610 16 18 20 22 24 26 28 Age years 30 32 34 36 38

deserves to be recognized 3 Outliers can greatly statistics such as the Mathematically an outlier is any number that is or the values of some summary and Example 1 Identifying Outliers Here again are the Cubs runs allowed data for cloudy day games Recall from the previous example that Q1 3 and Q3 6 0 1 1 2 3 3 3 3 3 3 4 4 4 4 4 4 5 6 6 6 6 9 9 10 11 13 14 1 Identify any outliers in the distribution Justify your answer 2 Boxplots A boxplot is used to summarize a distribution by displaying five key positions of data 1 3

To construct a boxplot follow these five steps 1 Draw a central box from the first quartile to the third quartile 2 Draw a vertical line segment in the box to mark the median 3 Use the 1 5IQR rule to identify possible outliers 4 Draw lines called whiskers that extend from the box out to the smallest and largest observations that are not outliers 5 If there are any outliers mark them separately 3 1 0 220 165 238 193 174 151 1 2 Example 2 Here again are the data showing the number of home runs hit by each Major League Baseball team in 2017 2 Identify if there are any outliers 186 219 212 192 224 206 224 189 200 128 196 228 237 222 232 168 223 186 221 194 241 1 Determine the five number summary for these data 3 3 Construct a boxplot to summarize this distribution 187 234 215

When finding the median of an will have two values at the of your in this case you find the To of into two find the true your two middle values This will divide your halves of equal number of values 0 0 1 2 2 2 3 3 3 4 5 5 5 5 8 11 12 15 Example 1 Mean versus Median Below are all the runs allowed by the Chicago Cubs on day games where it was cloudy in a recent season 0 4 6 4 4 3 14 11 2 3 10 4 6 6 4 9 1 3 9 3 6 1 13 4 5 3 3 1 Calculate the mean number of runs allowed in cloudy games

Problem 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

Decide whether a discrete or continuous random variable is the best model for each of the following variables a The number of cracks exceeding one half inch in 10 miles of an interstate highway b The weight of an injection molded plastic part c The number of molecules in a sample of gas d The concentration of output from a reactor

Customers are used to evaluate preliminary product designs In the past 95 of highly successful products received good reviews 60 of moderately successful products received good reviews and 10 of poor products received good reviews In addition 40 of products have been highly successful 35 have been moderately successful and 25 have been poor products a What is the probability that a product attains a good review b If a new design attains a good review what is the probability that it will be a highly successful product c If a product does not attain a good review what is the probability that it will be a highly successful product

The 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

The 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

Suppose 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

Level of Degree Male Female Total 405 665 804 1399 Associate 260 Bachelor s 595 Master s 230 Doctorate 25 Total 1110 329 PAND 23 1561 559 32 48 2671 2671 pariral A person who earned a degree in the year 2004 is randomly selected Find th probability of selecting someone who tuo a earned a bachelor s degree siqaris b earned a bachelor s degree given that the person is a female jelett sub dr Zauers c earned a bachelor s degree given that the person is not a female d earned an associate degree or a bachelor s degree e earned a doctorate given that the person is a male f earned a master s degree or is a female imeri og hlub w wot

2 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

Reminders Chi square is a form of statistical analysis used to compare the actual results observed with the expected results The equation tests the null hypothesis for the problem being analyzed The formula for Chi Square is X observed results expected results expected results The calculated X value is always compared to the degrees of freedom chart as seen on the right Unless instructed otherwise compare your value to the p 0 05 row Step 2 determine your expected values Step 3 complete the Chi square chart Observed O 1 A science teacher is bothered because of all the noise outside of his classroom each day He decides to see where the noise is coming from and finds that several groups of freshman students use the water fountain located by the door to his classroom There are three other water stations on campus and after studying the frequency at which students visit each water fountain he becomes convinced that students prefer the water fountain by his room rather than the other three fountains The teacher assigns a student to be at each water fountain and count the total number of students getting water from each one The data is as follows water fountain 1 by the teachers door 45 students water fountain 2 36 students water fountain 3 25 students and water fountain 4 30 students Is the teacher correct that students prefer to use the water fountain by his door Step 1 state the null hypothesis Expected E O E O E O E E Step 4 calculate your degrees of freedom P 0 05 0 01 Step 5 interpret results 1 2 3 84 5 99 6 64 9 32 CHI SQUARE TABLE Degrees of Freedom 5 6 7 3 7 82 9 49 11 07 12 59 14 07 15 51 11 34 13 28 15 09 16 81 18 48 20 09 Total