Statistics Questions and Answers

Robinson Crusoe Excerpt by Daniel Defoe My father told me it was men of desperate fortunes on one hand or of aspiring superior fortune on the other who went abroad upon adventures to rise by enterprise and make themselves famous in undertakings of a nature out of the common road that these things were all either toc far above me or too far below me that mine was the middle state or what might be called the upper station of low life which he had found by long experience was the best state in the world the most suited to human happiness not exposed to the miseries and hardships the labor and sufferings of the mechanic part of mankind and not embarrassed with the pride luxury ambition and envy of the upper part of mankind He told me I might judge of the happiness of this state by this one thing that this was the state of life which all other people envied that kings have frequently lamented the miserable consequence of being born to great things and wishec they had been placed in the middle of the two extremes between the mean and the great that the wise man gave his testimony to this as the standard of felicity when he prayed to have neither poverty nor riches He bade me observe it and I should always find that the calamities of life were shared among the upper and lower part of mankind but that the middle station had the fewest disasters and was not exposed to so many vicissitudes as the higher or lower part of mankind nay they were not subjected to so many distempers either of body or mind as those were who by vicious living luxury and extravagances on the one hand or by hard labor want of necessaries and mean or insufficient diet on the other hand bring distemper upon themselves by the natural consequences of their way of living that the middle station of life was calculated for all kind of virtue and all kind of enjoyments that peace and plenty were the handmaids of a middle fortune that temperance moderation quietness health society all agreeable diversions and all desirable pleasures were the blessings attending the middle station of life tha this way men went silently and smoothly through the world and comfortably out of it not embarrassed with the labors of the hands or of the head not sold to a life of slavery for daily bread nor harassed with perplexed circumstances which rob the soul of peace and the body C rest nor enraged with the passion of envy or the secret burning lust of ambition for great things but in easy circumstances sliding gently through the world and sensibly tasting the sweets of living without the bitter feeling that they are happy and learning by every day s experience to know it more sensibly 39 What message is the father trying to convey Being poor comes with hardships and a struggle for survival 8 The rich are unhappy because they lust for greater things Making a living for yourself will bring you happiness in life Living in the middle class means less hardships and high expectations 40 Based on details in the excerpt the reader can conclude that the father A use to be poor and now has a better understanding of how life works B is happy with his life but wishes his son would aspire for more in life does not understand why his con u

oday is the day I ve been working up to this moment all month long All year for that matte Today I sit with the jocks the most popular people at our school the highest of the Volleybal and Football Faction all together at one table Here goes The bell for lunch rings and I slowly pull myself out of my desk and drag my feet down the ha toward the cafeteria I can hear the blood pounding against the inside of my skull My fingers shake as I try to remember everything I ve learned what s truly important in making friends I sit down across from a Volleyball Girl Hey Maya what s up she asks smacking her neon pink chewing gum Hi Cristine can I sit here today I guess Thanks Carlos Sanchez stumbles in with his buddy Pablo singing The Lion Sleeps Tonight Badly He glances at me I freeze and force myself to smile even though I think I m going to be sick What s up Maya He rejoins the song then jumps back Holy crap Since when do you sit with us I try to stop my voice from shaking I ve sat with tons of people I point to the tables around the lunchroom The group seems impressed A football guy at the end of the table lear forward to see me Why I relax a little For fun Anyway I m moving to Georgia and WHAT YOU RE MOVING Carlos Sanchez shouts loud enough for the entire cafeteria to hear My dad got a job at a university there But you make our school look all smart and stuff And and now we re just gonna look dumb Carlos Sanchez will miss me too Am I dreaming Some of the boys get into an argument over who will miss me most No I want to sit next to Maya Too late I was here first I m floating honest to goodness floating My head has to be 50 feet above the earth 33 Which sentence shows that the narrator is not a popular student A I ve been working up to this moment all month long 8 Holy crap Since when do you sit with us But you make our school look all smart and stuff Some of the boys get into an argument over who will miss me most 34 What theme is explored in the excerpt A If you open up people will like you 8 Appearances can be deceiving Girls are capable of anything

TWIST Excerpt by Charles Dickens Poor Oliver He little thought as he lay sleeping in happy unconsciousness of all around him the board had that very day arrived at a decision which would exercise the most material influence over all his future fortunes But they had And this was it The members of this board were very sage deep philosophical men and when they came to turn their attention to the workhouse they found out at once what ordinary folks would never have discovered the po people liked it It was a regular place of public entertainment for the poorer classes a tavern where there was nothing to pay a public breakfast dinner tea and supper all the year round brick and mortar elysium where it was all play and no work Oho said the board looking very knowing we are the fellows to set this to rights we ll stop it all in no time So they established the rule that all poor people should have the alternative for they would compel nobody not they of being starved by a gradual process in the house or by a quick one out of it With this view they contracted with the water works to lay on an unlimited supply of water and with a corn factor to supply periodically small quantities of oatmeal and issued three meals of thin grue a day with an onion twice a week and half a roll of Sundays They made a great many other wise and humane regulations having reference to the ladies which it is not necessary to repeat kindly undertook to divorce poor married people in consequence of the great expense of a suit in Doctors Commons and instead of compelling a man to support his family as they had theretofore done took his family away from him and made him a bachelor There is no saying how many applicants for relief under these last two heads might have started up in all classes of society if it had not been coupled with the workhouse but the board were long headed men and had provided for this difficulty The relief was inseparable from the workhouse and the gruel and that frightened people 35 The excerpt is important to the development of the plot because it A signifies the point at which Oliver s life changes presents the community s opinion on poverty explains how the workhouse changed provides a solution to the problems of the poor 6 Which detail from the excerpt shows that the poor will suffer under the changes Oho said the board looking very knowing we are the fellows to set this to rights we ll stop it all in no time So they established the rule that all poor people should have the alternative of being starved by a gradual process in the house or by a quick one out of it With this view they contracted with the water works to lay on an unlimited sunplu

Read the selection and choose the best answer to each question Twelves Years a Slave Excerpt by Solomon Northup While living at the United States Hotel I frequently met with slaves who had accompanied their masters from the South They were always well dressed and well provided for leading apparently an easy life with but few of its ordinary troubles to perplex them Many times they entered into conversation with me on the subject of Slavery Almost uniformly I found they cherished a secret desire for liberty Some of them expressed the most ardent anxiety to escape and consulted me on the best method of effecting it The fear of punishment however which they knew was certain to attend their re capture and return in all cases proved sufficient to deter them from the experiment Having all my life breathed the free air of the North and conscious that I possessed the same feelings and affections that find a place in the white man s breast conscious moreover of an intelligence equal to that of some men at least with a fairer skin I was too ignorant perhaps too independent to conceive how any one could be content to live in the abject condition of a slave I could not comprehend the justice of that law or that religion which upholds or recognizes the principle of Slavery and never once I am proud to say did I fail to counsel any one who came to me to watch his opportunity and strike for freedom 31 Which phrase from the excerpt suggests the narrator cannot fulling understand what slaves experience A Some of them expressed the most ardent anxiety to escape and consulted me on the best method of effecting it B The fear of punishment however which they knew was certain to attend their re capture and return in all cases proved sufficient to deter them from the experiment Having all my life breathed the free air of the North and conscious that I possessed the same feelings and affections that find a place in the white man s breast conscious moreover of an intelligence equal to that of some men at least with a fairer skin I was too ignorant perhaps too independent to conceive how any one could be content to live in the abject condition of a slave 32 What does the excerpt reveal about the narrator He is willing to help no matter what the risk B He has always lived a life of true freedom He believes some slaves are happy and treated well He soos

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You must estimate the mean temperature in degrees Fahrenheit with the following sample temperatures 67 3 76 6 90 7 68 4 72 1 69 3 86 5 89 66 1 Find the 95 confidence interval Enter your answer as an open interval This means enter your answer inside of parentheses accurate to two decimal places For example if the lower limit is 12 23 and the upper limit is 15 31 enter your answer as 12 23 15 31 95 C I Answer should be obtained without any preliminary rounding Did you remember to enter your DROWNor inton

Express the confidence interval 295 5 149 in the form of a trilinear inequality That means type your lower limit of the interval in the first box and your upper limit of the interval in the second box F

A random sample of 6 fields of corn Determine the 95 confidence inte

How will increasing the level of confidence without changing the samp mean Assume that the population standard deviation is unknown an Select your answer from the choices below Answer O The margin of error will decrease because the critical va cause the confidence interval to be narrower

How will decreasing the level of confidence without changing the sample size affect the width of a confidence interval for a population mean Assume that the population standard deviation is unknown and the population distribution is approximately normal Select your answer from the choices below Answer Tables Keypad Keyboard Shortcuts The margin of error will increase because the critical value will increase The increased margin of error will cause the confidence interval to be wider The margin of error will decrease because the critical value will decrease The decreased margin of error will cause the confidence interval to be narrower The margin of error will increase because the critical value will decrease The increased margin of error will cause the confidence interval to be wider The margin of error will decrease because the critical value will increase The decreased margin of error will cause the confidence interval to be narrower

22704 1 2 K Que The bar graph below shows that as costs c group of people devoted less of their budge

The executives at HyGreat a soda and energy drink company conducted a quarterly review of the company s production facilities For the review the number of work stoppages due to mechanical failure were counted at each of the company s bottling plants The histogram below summarizes the data Use the histogram to answer each of the questions Frequency Number of bottling plants 10 9 8 7 6 5 4 3 2 4 to 10 11 to 17 18 to 24 Number of work stoppages a What is the class width 25 to 31 b One class is the least frequent How many bottling plants are in this class 1 5 c How many bottling plants had 18 or more work stoppages

Ques Fill in each blank so that the resulting stater

ion 7 2 K How wide is the chasm between wh the workplace According to a 2015 group women lose 435 049 over t pay gap The bar graph to the right United States for men and

1 Data on grade point averages and hours sp following results where y denotes GPA and x y 2 400x Due d 1 x x 900 Compute the least squares estimates of

A Food Marketing Institute found that 29 of households spend more than 125 a week on groceries Assume the population proportion is 0 29 and a simple random sample of 215 households is selected from the population What is the probability that the sample proportion of households spending more than 125 a week is less than 0 26 probability that the sample proportion of households spending more than 125 a week is There is a less than 0 26 Round the answer to 4 decimal places mut

In an election suppose that 65 of voters support the incumbent candidate If we poll 169 of these voters at random the probability distribution for the proportion of the polled voters that support the incumbent candidate can be modeled by the normal distibution pictured below Complete the boxes accurate to two decimal places

A population of values has a normal distribution with 77 and 95 1 a Find the probability that a single randomly selected value is between 39 3 and 75 2 Round your answer to four decimal places P 39 3 X 75 2 b Find the probability that a randomly selected sample of size n 28 has a mean between 39 3 and 75 2 Round your answer to four decimal places P 39 3 M 75 2

In an election suppose that 60 of voters support a school levy increase If we poll 201 of these voters at random the probability distribution for the proportion of the polled voters that support a school levy increase can be modeled by the normal distibution pictured below Complete the boxes accurate to two decimal places

The city of Raleigh has 8 300 registered voters There are two candidates for city council in an upcoming election Brown and Feliz The day before the election a telephone poll of 350 randomly selected registered voters was conducted 188 said they d vote for Brown 141 said they d vote for Feliz and 21 were undecided Give the sample statistic for the proportion of voters surveyed who said they d vote for Brown Round your answer to four decimal places This sample statistic suggests that we might expect voters to vote for Brown of the 8 300 registered

A random sample of size n 658 from a population whose parameter is p 0 45 a What is the mean of the distribution of sample proportions Round the answer accurate to 2 decimal places Hp b What is the standard deviation of the distribution of sample proportions Round the answer accurate to 2 decimal places op

The following is a random sample of the annual salaries of hig salaries is approximately normal construct a 99 confidence interval for the mean salary of high school 35 940 32 310 56 1 nswer

A local recreational basketball league takes their statistics seriously Luis the league s data analyst tracked the number of three point shots attempted by each team over the last season The histogram below summarizes the data Use the histogram to answer each of the questions Frequency Number of teams 10 9 8 7 6 5 44 3 2 1 210 to 284 285 to 359 360 to 434 435 to 509 510 to 584 Number of three point attempts a One class is the most frequent How many teams are in this class 0 b According to the histogram what is the total number of teams 0 c What is the class width 0

In late August of last year Pie Dee Restaurant sponsored its first pizza eating contest For the contest the number of slices of cheese pizza eaten by each contestant were counted The histogram below summarizes the data Use the histogram to answer each of the questions Frequency Number of contestants 10 9 8 7 6 5 4 3 24 14 6 to 10 11 to 15 16 to 20 21 to 25 26 to 30 Number of pizza slices a How many contestants ate from 11 to 15 pizza slices 0 b What is the class width 0 c How many contestants ate 16 or more pizza slices 0

Each summer track and field athletes from all over the world represent their country by competing in the Sekai Games At the end of last year s games the official record keeper counted the number of gold medals won by each country in that year s games The histogram below summarizes the data Use the histogram to answer each of the questions Frequency Number of countries 10 9 8 7 6 5 4 3 2 3 to 6 7 to 10 11 to 14 Number of gold medals 15 to 18 a What is the class width b How many countries won 10 or fewer gold medals 0 c One class is the most frequent How many countries are in this class

Goran is the manager for the touring rock band Hi Phone For the band s recently ended summer tour Goran kept track of the attendance of each of the band s concerts The histogram below summarizes the data Use the histogram to answer each of the questions Frequency Number of concerts NO 9 8 7 6 5 44 3 2 1 0 175 to 299 300 to 424 Number of people who attended 50 to 174 a What is the class width 0 425 to 549 b How many concerts were attended by from 300 to 424 people 0 c According to the histogram what is the total number of concerts

Saltare is a maker of high end apparel for women For market research one afternoon Saltare s sales tea surveyed adult women at a busy airport on the number of blouses they own The histogram below summarizes the data Use the histogram to answer each of the questions Frequency Number of adult women 10 9 8 7 6 5 4 3 2 1 0 11 to 19 20 to 28 29 to 37 38 to 46 Number of blouses owned 47 to 55 a How many adult women in the survey own from 38 to 46 blouses 0 b What is the class width 0 c How many adult women in the survey own 37 or fewer blouses

The numbers of students in the 9 schools in a district are given below Note that these are already ordered from least to greatest 164 199 232 242 257 266 292 373 405 Send data to calculator Suppose that the number 164 from this list changes to 290 Answer the following a What happens to the median b What happens to the mean It decreases by 0 It increases by 0 It stays the same It decreases by It increases by O It stays the same 0 17 0

of success p 0 40 If necessary consult a list of formulas a Find y the mean of X Do not round your answer Hx b The histograms of three binomial distributions are shown below Choose the one that could be the histogram of the distribution of x 0 20 0 15 0 10 0 05 Histogram A 0 20 0 15 0 10 X 0 05 Histogram B O 0 20 0 15 0 10 0 05 Histogram C

Consider the graph below population increase millions 100 90 80 70 60 50 40 30 20 10 0 1950 World Population Increase 1960 1980 1990 source U S Bureau of the Census International Data Base via GeoHive 1970 year Use interval notation to give the Domain Years y Range Population in millions P 2000

Question 15 Itranscript n a certain town 40 of adults have a college degree Suppose four adults are randomly Fill in the probability distribution table of x What is the expected value of x Give answ K A D P x

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ShortStry and Nquiry are two social media apps in which users can post messages in text The character counts for posts on ShortStry have a population mean of 313 and a standard deviation of 41 The character counts for posts on Nquiry have a population mean of 267 and a standard deviation of 53 For each app the distribution of the character counts is clearly bell shaped Karen s last post on ShortStry was 411 characters Kala s last post on Nquiry was 212 characters a Find the z scores of Karen s last post as a post on ShortStry and Kala s last post as a post on Nquiry Round your answers to two decimal places z score of Karen s post z score of Kala s post X b Relative to its population which post was longer Choose the best answer based on the z scores of the two posts O Karen s post O Kala s post O It is unclear which post was longer relative to its population X

At an unconventional casino you bet on the roll of an 17 sided die If you roll a 7 you win 2 If you roll a 1 or 17 you win 7 If you roll a 13 you lose 2 If you roll any other number you lose 1 to the casino Let X denote the amount of money you win from playing this game once a Fill in the table to create a probability distribution for X Use fractions or decimals rounded to three decimal places when necessary Please enter values into the table as they were introduced in the paragraph above P x X b Find the expected profit Round to the nearest cent two decimal places Is this game profitable for you How does the expected value tell you whether it is profitable or not

Consider the following situations and whether they are examples of a binomial distribution a It is supposed that 20 of people have a favorite color of blue that 10 have a favorite color of red and that 5 of people have a favorite color of yellow A random sample of 500 Americans are asked what their favorite color is Yes this is an example of a binomial distribution O No this is NOT an example of a binomial distribution b It is supposed that 15 of Americans smoke cigarettes A random sample of 200 Americans are asked if they smoke cigarettes No this is NOT an example of a binomial distribution Yes this is an example of a binomial distribution c Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed O No this is NOT an example of a binomial distribution Yes this is an example of a binomial distribution d For the situations above that were NOT binomial explain why they were not binomial

A researcher believes that 48 5 of people who grew up as the only child have an IQ score over 100 However unknown to the researcher this figure is actually 50 which is the same as in the general population To attempt to find evidence for the claim the researcher is going to take a random sample of 400 people who grew up as the only child Let p be the proportion of people in the sample with an IQ score above 100 Answer the following If necessary consult a list of formulas a Find the mean of p b Find the standard deviation of p c Compute an approximation for P 0 485 which is the probability that there will be 48 5 or more people with IQ scores over 100 in the sample Round your answer to four decimal places X

Manolo is an adult male shark that is 3 1 meters long and Lydia is an adult female shark that is 4 1 meters long The distribution of the lengths of the adult female sharks in the aquarium is clearly bell shaped The same is true for the distribution of the lengths of the adult male sharks in the aquarium The aquarium s adult female shark population has a mean length of 3 53 meters and a standard deviation of 0 51 meters The aquarium s adult male shark population has a mean length of 2 67 meters and a standard deviation of 0 29 meters a Find the z scores of Manolo s length as an adult male shark at the aquarium and Lydia s length as an adult female shark at the aquarium Round your answers to two decimal places z score of Manolo s length z score of Lydia s length X b Relative to its population which is smaller Choose the best answer based on the z scores of the two lengths O Manolo O Lydia O It is unclear which shark is smaller relative to its population X

True or false The normal distribution appears naturally in the world

T10 using the Trapezoidal rule for int 0 1 e x d x Find the actual error produced in using this method of approximation b Find the upper bound on the error term ET and compare this to the actual error you found in part a c How large do we need to choose n to guarantee the estimate of In for the integral in part a is accurate to 0 00001 Round all answers in parts a

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The density of air at 20 C and 1 00 atm is 1 205 g L If this air were compressed at the same temperature to equal the pressure at 23 0 m below sea level what would be its density Assume the barometric pressure is constant at 1 00 atm The density of seawater is 1 025 g cm Density g L

B C LO 5 7 A E FIGURE P1 11 F P 21 m 1 11 Determine length ED for the similar triangles shown in Figure P1 11

Refer to the accompanying data set of 20 randomly selected presidents Treat the data as a sample an construct a 95 confidence interval estimate of the population percentage Based on the result does i Click the icon to view the table of heights COLD Construct a 95 confidence interval estimate of the percentage of presidents who were taller than thei p Round to one decimal place as needed President ar PRESIDENT G H W Bush Taylor J Q Adams Jefferson Cleveland Pierce Harrison Coolidge Buchanan J Adams Lincoln

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A study of migraine states that a total of 140 patients with migraine without aura were recruited and assigned randomly to 2 different groups the acupuncture group treated with verum acupuncture plus placebo and the control group treated with sham acupuncture plus flunarizine This is a longitudinal cohort a cross sectional survey anecdotal evidence a matched pairs experiment a completely randomized experiment a case control study O a voluntary sample