Statistics Questions and Answers

Adult men have heights with a mean of 69 0 inches and a standard deviation of 2 8 inches Find the z score of a man 68 7 inches tall to 2 decimal places

6 hour period The percentage data are the percentages of fishermen who caught x fish in a 6 hour period while fishing from shore P X P X 0 5 0 4 0 3 0 2 0 1 0 a Convert the percentages to probabilities and make a histogram of the probability distribution Because the data table has summarized the data into categories use SALT to create a bar chart 0 5 0 4 0 3 0 2 0 1 0 0 1 43 37 12 USE SALT 0 2 0 1 LI 1 2 X 3 2 7 X at least 4 1 3 at least 4 3 at least 4 P X P 0 5 0 4 0 3 0 2 0 1 0 0 5 0 4 0 3 0 2 0 1 0 0 1 0 1 2 X 2 X 3 at least 4 3 at least 4 b Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6 hour period c Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6 hour period d Compute the expected value of the number of fish caught per fisherman in a 6 hour period round at least 4 to 4 fish e Compute the standard deviation of the number of fish caught per fisherman in a 6 hour period round at least 4 to 4 Round your answer to three decimal places 7 fish

roblem 6 Note that this question along with all other problems that don t have the symbol beside them should be done by hand Consider the following data Problem 6 a Problem 6 b Problem 6 c Problem 6 d Problem 6 e 42 68 57 64 40 43 49 63 53 47 a Draw a stem and leaf plot including depths using intervals of length 5 See the bottom of this example for an explanation of depths Enter the value of the depths only in the answer box below For example if your stem and leaf plot looked like the one at the bottom of this example then you would enter the following numbers into the answer box 8 36 20 44 21 5 1 b Calculate the mean c Calculate the sample variance d Calculate the range e Calculate the coefficient of variation XXXX depths separated with commas mean rounded to 2 decimals sample variance rounded to 2 decimals range coefficient of variation

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 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

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

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

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

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

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

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

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

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

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

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

1 To remove impediments 2 To enable cooperation across all roles and functions 3 To organize and facilitate the sprint planning meeting 4 To protect the team from both external and internal interferences

The director of a hospital pharmacy chooses at random 100 people age 60 or older from each of three surrounding counties to ask their opinion of a new prescription drug program Identify the population in the study People age 60 and older from and sample Select Select People age 60 and older that are customers of the pharmacy People age 60 and older from 3 counties People age 60 and older 100 people age 60 and older from 3 counties

55 50 45 8 Thousands of dollars per year 9 25 20 15 10 5 10 12 14 16 What is wrong with this graph 18 20 Years 22 OIt uses different scales on the two axes 24 26 28 O It doesn t label the variables on the two axes O It gives no information about the units for the variables 30

SPEED Feet per second 8 18 16 14 12 1 8 9 4 2 O 4 2 4 5 6 TIME Seconds me area of the shaded quadrilateral is feet he area of the quadrilateral corresponds to the 7 8 6 10 between second 0 and second second 2 and second second 2 and second second 0 and second

Do bonds reduce the overall risk of an investment portfolio Let x be a random variable representing annual percent return for Vanguard Total Stock Index all stocks Let y be a random variable representing annual return for Vanguard Balanced Index 60 stock and 40 bond For the past several years we have the following data x 120 35 35 20 30 24 23 12 12 22 y 10 a Compute Ex Ex 98 LAUSE SALT Compute Ex Ex 4546 Compute y Sy 86 Compute Ey Sy2 2260 s 2 30 12 21 17 15 2 s 358 56 x S 18 9357 x 152 04 1 4 b Use the results of part a to compute the sample mean variance and standard deviation for x Round your answers to four decimal places X 9 8 Use the results of part a to compute the sample mean variance and standard deviation for y Round your answers to four decimal places y 8 6 x S 12 3304 x 3 12 c Compute a 75 Chebyshev interval around the mean for x values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places x Use the intervals to compare the two funds Compute a 75 Chebyshev interval around the mean for y values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places k 2 75 of the returns for the balanced fund fall within a narrower range than those of the stock fund O 75 of the returns for the stock fund fall within a narrower range than those of the balanced fund O 25 of the returns for the balanced fund fall within a narrower range than those of the stock fund 25 of the returns for the stock fund fall within a wider range than those of the balanced fund x d Compute the coefficient of variation in percent for fund x Round your answer to the nearest whole number X Use the coefficients of variation to compare the two funds For each unit of return the stock fund has lower risk For each unit of return the balanced fund has lower risk For each unit of return the funds have equal risk Compute the coefficient of variation in percent for fund y Round your answer to the nearest whole number If s represents risks and represents expected return then s x can be thought of as a measure of risk per unit of expected return In this case why is a smaller CV better Explain

The measure of standard error can also be applied to the parameter estimates resulting from linear regressions For example consider the following linear regression equation that describes the relationship between education and wage WAGE Bo B EDUC where WAGE is the hourly wage of person i i e any specific person and EDUC is the number of years of education for that same person The residual e encompasses other factors that influence wage and is assumed to be uncorrelated with education and have a mean of zero Suppose that after collecting a cross sectional data set you run an OLS regression to obt Following parameter estimates WAGE 10 1 6 2 EDUC 4 86 3 52 4 19 5 53 If the standard error of the estimate of 1 is 1 34 then the true value of lies between and grows you would expect this range to in size As the number of observations in a data set

It s no surprise that high school students get less sleep than middle school students the distributions of the number of hours of sleep differs in other ways as well Whi data set the number of hours of sleep for high school students or middle school students would you expect to have a larger standard deviation and why Choose a that apply Some high school students sleep for long periods of time High school students have a larger standard deviation Middle school students have a larger standard deviation The average amount of sleep high schoolers get is more than middle schoolers Most middle school students sleep a similar amount of time Some high school students sleep very little

2 The different types of data Suppose you have the following data set which shows information about the inflation rate and gross domestic product GDP rate for the same group of countries over several years The following is an example of such a data set Inflation Percent 1 1 1 4 1 3 2 1 3 2 4 4 3 2 2 1 3 6 GDP Trillions of dollars 12 12 3 12 2 8 1 9 2 11 2 16 1 14 2 15 9 Y Country ID 1 1 1 The previous data set can best be classified as a 2 2 WWN 3 A Time Period 2017 2018 2019 2017 2018 2019 2017 2018 2019 data set

Suppose there is a disease certain to impact exactly 5 of a population and that each member of the population is equally likely become infected Treatment for individuals who are infected costs 32 000 Assume in this scenario that the necessary treatment for the disease is the only healthcare cost faced by this population to pay the expected cost of healthcare with The expected cost of healthcare is If members of the population do not prefer certainty rather than take on the 5 risk of having to pay the full cost of the treatment they are risk averse

1 The value of insurance Suppose your classmate Roby is faced with the following decision they either receive 6 000 with certainty or a 50 50 chance of receiving 3 000 or 9 000 Suppose Roby prefers the certain 6 000 True or False Based on their preferences Roby is a risk averse person O True O False

Using the Child Development dataset in the Math 12 group in StatCrunch construct 2 boxplots using weight age 9 variable for each males and females Compare the 2 boxplots Choose the correct statement from the following O The distribution of both males and females weight at age 9 is symmetric with outliers with the median at 31 kg Males have a smaller IQR M 4 5 F 6 9 but larger range M 46 9 F 25 7 than females The typical interval for males 28 8 33 3 significantly overlaps the typical interval for females 27 6 34 5 O The distribution of both males and females is symmetric with the median at 25 kg and both have outliers above and below the median The spread is the same IQR 4 5 and the typical intervals overlap significantly O The distribution of both males and females weight at age 9 is right skewed with the median at 31 kg and the same IQR of 4 5 Males typical interval 19 9 28 8 does not overlap the female typical interval 34 5 47 4 O The distribution of males is symmetric while the distribution of females is right skewed The median is 31 kg and the IQR is 6 9 with outliers for both males and females Males has a higher maximum than females

This boxplot shows the distribution of backpack weights for a sample of elementary schooll children What is the interquartile range 5 10 15 20 25 30 35 40 O about 9 pounds O about 14 O about 36

You see a classmate in front of the art building occasionally stopping students and asking them questions He happens to stop you and you ask what he s doing He says that he is working on an assignment for his statistics class He is collecting student opinions about the college However he only has time before his art class to conduct the survey You tell him that he should use a random sample instead of occasionally stopping students as they enter the art building He replies Why should I use a random sample This is so much easier Which of the following statements should you include in your explanation Check all that apply If you use a random sample you are more likely to avoid bias in the survey results In a random sample some members of the student population are less likely to be selected than others O A random sample will be representative of the student population A random sample allows you to draw conclusions about the opinions of all students at your college

In 1912 the RMS Titanic a British passenger ship sank in the North Atlantic Ocean after colliding with an iceberg Historians do not know the exact passenger list so the death toll is estimated Here is the data from 1 995 passengers on board by cabin class Observed Counts First Class Second Class Third Class Crew Row Totals Died Survived 241 Column Totals Question 12 O2 17 134 O 0 42 1 35 163 83 627 209 421 Using the chart above which of the following could be used to communicate the risk of death for a Crew member compared to a First Class passenger 117 0 5 pts

Assume that the following histograms are drawn on the same scale III II O Histogram I O Histogram II O Histogram III IV Which one of the histograms has a mean that is smaller than the median

Which histogram shows a distribution of exam scores on an easy exam I O Histogram I O Histogram II O Histogram III O Histogram IV 111 IV 11

A student conducted a survey on male and female driving habits by randomly selecting 25 males and 25 females as they left campus Identify the sampling method used O Stratified Sample O Convenience Sample O Simple Random Sample Cluster Sample

Random assignment is used to eliminate confounding variables by making the groups similar through randomization of the groups True or False O True O False