Statistics Questions

color in the second generation of a certain cross of sweet peas should be red or white in a 3 1 ratio That is each plant has probability 3 4 of having red blossoms and the blossom colors of separate plants are independent blickwinkel Alamy a What is the probability that exactly three out of four of these plants have red blossoms b What is the mean number of red blossomed plants when 60 plants of this type are grown from seeds c What is the probability of obtaining at least 45 red from

Comment on the quotation below from a climatologist What I think is our best determination is it will be a colder than normal winter said Pamela Naber Knox a Wisconsin state climatologist I m basing that on a couple of different things First in look at the past few winters there has been a lack of really cold weather Even though we are not supposed to use the law of averages we are due Choose the correct answer below OA There is no Law of Averages She would be wrong to think they are due for a harsh winter OB The climatologist s prediction is probably wrong Since the past few winters have not had very cold weather it is more likely that the next winter will also not have very cold weather OC The climatologist is likely inaccurate Weather is too naturally unpredictable for forecasting to be reliable OD The climatologist is right in her assessment that she should not use the Law of Averages Her forecast for colder weather is likely accurate

The plastic arrow on a spinner for a child s game stops rotating to point at a color that will determine what happens next Are the given probability assignments possible Why or why not a Since 5 Since C Since d Since e Since the sum of the probabilities is less than 1 the sum of the probabilities is less than 1 at least one probability is not between 0 and 1 this probability assignment the sum of the probabilities is greater than 1 each probability is between 0 and 1 and the sum of the probabilities is 1 this probability assignment ability assignment ability assignment ability assignment is possible possible possible V possible possible a b c d e Red 1 0 25 0 4 0 4 0 5 Yellow Green 0 0 25 0 0 25 0 2 0 2 0 3 1 1 0 2 0 1 Blue 0 0 25 0 3 1 8 0 2

If p value of a statistical test is 0 04 and alpha is 0 10 you Multiple Choice O have insufficient evidence to either reject or fail to reject the null hypothesis should reject the null hypothesis i e significant result should fail to reject the null hypothesis i e not significant result accept the alternate hypothesis

to review Examples 7 7 7 8 and 7 9 7 2 before attempting these problems Review Constants A lightweight vertical spring of force constant k has its lower end mounted on a table You compress the spring by a distance d place a block of mass m on top of the compressed spring and then release the block The spring launches the block upward and the block rises to a maximum height some distance above the now relaxed spring Find the speed of the block just as it loses contact with the spring Express your answer in terms of the variables m d and constants g k xa A O Xb 06 a x x X X IXI X 10n X med

Every morning my neighbor goes out walking I observe that 20 of the time she walks with her beagle 70 of the time she walks with her golden retriever and 30 of the time she walks alone What is the probability she walks both dogs at the same time Hint use the general addition rule Choose the correct answer below O A 20 B 30 OC 70 OD There is not enough information to answer the question

Suppose that 22 of people have a dog 27 of people have a cat and 15 of people own both What is the probability that someone owns a dog or a cat The probability of a person having a dog or a cat is

A casino claims that its roulette wheel is truly random What should that claim mean Choose the correct answer below OA The same number will not come up twice in a row OB The probabilities of all numbers will add to 1 OC Every number will occur before any numbers repeat O D Every number is equally likely to occur

In a dresser are ten blue shirts seven red shirts and eight black shirts a What is the probability of randomly selecting a red shirt b What is the probability that a randomly selected shirt is not black a The probability of randomly selecting a red shirt is Type an integer or a decimal Do not round b The probability that a randomly selected shirt is not black is Type an integer or a decimal Do not round

Suppose that 65 of families living in a certain country own a laptop and 22 own a desktop computer The Addition Rule might suggest then that 87 of families own either a laptop or a desktop computer What s wrong with that reasoning Choose the correct answer below CCIDE OA The sum of the probabilities of the two given events does not equal 1 so this is not a legitimate probability assignment OB If one family owns a laptop or a desktop computer it can influence another family to also own a laptop or a desktop computer The events are not independent so the Addition Rule does not apply OC The reasoning is correct Thus 87 of families own either a laptop or a desktop computer OD A family may own both a laptop and a desktop computer The events are not disjoint so the Addition Rule does not apply

33 Hyundai sales in 2015 Hyundai Motor America sold 761 710 vehicles in the United States in 2015 with the U S built Elantra leading sales with 241 706 cars sold The other top selling nameplates in 2015 were the Sonata with 213 303 sold the Santa Fe with 118 134 sold and the Tucson with 63 591 sold The company wants to undertake a survey of 2015 Hyundai buyers to ask them about satisfaction with their purchase a What proportion of the Hyundais sold in 2015 were Elantras b If they plan to survey a simple random sample of 1000 Hyundai buyers what is the expected number and standard deviation of the number of Elantra buyers in the sample c What is the probability they will get fewer than

aerosolized vaccine for measles was developed in Mexico and has been used on more than 4 million children since 1980 Aerosolized vaccines have the advantages of being able to be administered by people without clinical training and do not cause injection associated infections The percentage of children developing an immune response to measles after receiving the subcutaneous injection of the vaccine is 95 and for those receiving the aero solized vaccine it is 85 There are 20 children to be vaccinated for measles using the aerosolized vaccine in a small rural village in India We are going to count the num ber who devel im oped an mune response to measles after vaccination Dr P Marazzi Science Source a Explain why this is a binomial setting b What is the probability that at least one child does not develop an immune response to measles after receiving the aerosolized vaccine What would be the probability that at least one child does not develop an immune response to measles if all children were

11 College Admissions A small liberal arts college in Ohio would like to have an entering class of 450 students next year Past experience shows that about 37 of the students admitted will decide to attend The college is planning to admit 1175 students Suppose that students make their decisions independently and that the probability is 0 37 that a randomly chosen student will accept the offer of admission a What are the mean and standard deviation of the number of students who accept the admissions offer from this college b Use the Normal approximation to approximate probability that the college gets more students than it wants Be sure to check that you can safely use the approximation c Use software or an online binomial calculator to compute the exact prob ability that the college gets more students than it wants How good is the approximation in part b d To decrease the probability of getting more students than are wanted does the college need to increase or decrease the number of students it admits Using software or an online binomial calculator what is the larg est number of students that the college can admit if administrators want the exact probability of getting more students than they want to be no

tion in the Search box a Enter 5 choose 2 and click Search What does Google return b You see that Google calculates the binomial coefficient 5 choose 2 What are the values of the binomial coefficients for 500 choose 2 and 500 choose 100 We expect that there are more ways to choose 100 than to choose 2 but how many more may be a surprise That e 107 in Google s answer means a 1 followed by 107 zeros c Google also does binomial probabilities Enter 10 choose 1 0 11 0 89 9 to find P X 1 in Example 14 5 page 336 What is

3 Boxes of Tiles Boxes of 6 inch slate flooring tile contain 40 tiles per box The count X is the number of cracked tiles in a box You have noticed that most boxes contain no cracked tiles but if there are cracked tiles in a box then there are usually several

In each of Exercises 14 1 through 14 3 X is a count Does X have a binomial distribution Give your reasons in each case 14 1 Working Cell Numbers When an opinion poll selects cell phone numbers at random to dial the cell phone exchange is first selected and then random digits are added to form a complete telephone number see Example 8 5 page 212 When using this procedure to generate random cell phone numbers approxi mately 55 of the cell numbers generated correspond to working numbers You watch a pollster dial 15 cell numbers that have been selected in this manner X is the number that correspond to a working number

1 13 pts After a survey where students had to pick favorite preferred genre of music We put their results in the table below If we select one studen from our survey at random find the probability that they Note give your solutions both as unreduced fractions and decimals rounded to 4 decimal places Rap Rock Country Total 25 90 9 3 37 Comedy 30 35 Drama 16 19 Horror 9 TOTAL 50 63 Prefer Comedy 90 150 0 6000 of students preferring comedy total of students Prefer Rap of students preferring rap total of students 500 3 0 3333 Prefer anything but Rap of students preferring rock and country total of students 63 37 100 150 150 0 6667 Prefer both Rock AND Drama of students preferring rock and drama total of students P rock n drama 150 0 1267 Prefer Rock OR Drama P rock P drama P rock drama 630 150 150 44 44 16 150 63 44 19 150 107 19 88 150 150 Prefer Rock GIVEN that they prefer Drama 0 5867 Prefer Ran OR Prefers Comedy di imp TT 1 11 er Coming 16 E rfs 1 1 i h 1 Itte il 1 4

A A 16 18 16 CA AR 22 2 412 A2 32 32 02 A2 VE 2 23 38 4 28 4 32 Jacks afa afla a 733 32 97 2 6 pts For the following questions we are considering a standard deck of cards I have included an image fo your reference What is the probability that we will draw a face card total of face cards 12 ser 4 Kings ila a 12 33 Probability of drawing face card total of cards 52 What is the probability that we will draw a face card given that the card we drew is a club

A random sample of rivers on the South Island of New Zealand was measured in km The lengths of rivers flowing to the Pacific Ocean had a mean of 131 82 km and a standard deviation of 78 85 km and the lengths of rivers flowing to the Tasman Sea had a mean of 68 44 km and a standard deviation of 68 78 km Which of the following statements best compares the means Select an answer Which of the following statements best compares the standard deviations Select an answer The lengths of rivers flowing to the Pacific Ocean had a higher average than the lengths of rivers flowing to the Tasman Sea The lengths of rivers flowing to the Pacific Ocean had a lower average than the lengths of rivers flowing to the Tasman Sea The middle of the lengths of rivers flowing to the Pacific Ocean was higher than the middle of the lengths of rivers flowing to the Tasman The middle of the lengths of rivers flowing to the Pacific Ocean was lower than the middle of the lengths of rivers flowing to the Tasman The lengths of rivers flowing to the Pacific Ocean were more consistent than the lengths of rivers flowing to the Tasman Sea The lengths of rivers flowing to the Pacific Ocean were less consistent than the lengths of rivers flowing to the Tasman Sea

To determine if Reiki is an effective method for treating pain a pilot study was carried out where a certified second degree Reiki therapist provided treatment on volunteers Pain was measured using a visual analogue scale VAS immediately before and after the Reiki treatment Olson Hanson 1997 and the data for a random sample of volunteers were recorded The VAS readings before the Reiki treatment had a mean of 3 15 and a standard deviation of 2 19 and VAS readings after the Reiki treatment had a mean of 2 83 and a standard deviation of 2 09 Which of the following statements best compares the means Select an answer Which of the following statements best compares the standard deviations Select an answer The VAS readings before the Reiki treatment had a higher average than the VAS readings after the Reiki treatment The VAS readings before the Reiki treatment had a lower average than the VAS readings after the Reiki treatment The middle of the VAS readings before the Reiki treatment was higher than the middle of the VAS readings after the Reiki treatment The middle of the VAS readings before the Reiki treatment was lower than the middle of the VAS readings after the Reiki treatment The VAS readings before the Reiki treatment were more consistent than the VAS readings after the Reiki treatment The VAS readings before the Reiki treatment were less consistent than the VAS readings after the Reiki treatment

For the data shown above find the following Round answer in the first blank to 3 decimal place s In the second blank put the correct units Find the mean 3 568 Find the median Find the range Enter an integer or decimal number more Find the standard deviation 5 36 0 20 2 86 3 46 1 46 7 93 1 80 7 84 2 87 6 72 0 14 5 86 0 78 0 79 0 28 0 86 5 93 9 11 1 45 7 32 2 27 1 36 2 45 2 62 7 48 metric tons per capita metric tons per capita metric tons per capita metric tons per capita

ww wamap org assess2 cid 33962 aid Lengtns or a random sample of 15 rivers on the south island or New Zealand that flow to the Pacific Ocean km or kilometers are listed in the table below For the data shown above find the following Round answer in the first blank to 1 decimal place s In the second blank put the correct units I Find the mean 110 3 Find the median 90 Find the range Length 80 48 95 64 72 64 288 90 138 209 56 121 97 169 64 Find the standard deviation

Pulse rates in bpm were collected from a random sample of females who are non smokers but do drink alcohol The pulse rates before they exercised had a mean of 75 74 and a standard deviation of 10 43 The pulse rates after they ran in place for one minute had a mean of 126 06 and a standard deviation of 24 55 Which of the following statements best compares the means Select an answer Which of the following statements best compares the standard deviations Select an answer The pulse rates before they exercised had a higher average than the pulse rates after they ran in place for one minute The pulse rates before they exercised had a lower average than the pulse rates after they ran in place for one minute The middle of the pulse rates before they exercised was higher than the middle of the pulse rates after they ran in place for one minute The middle of the pulse rates before they exercised was lower than the middle of the pulse rates after they ran in place for one minute The pulse rates before they exercised were more consistent than the pulse rates after they ran in place for one minute The pulse rates before they exercised were less consistent than the pulse rates after they ran in place for one minute

sample of Print O Matic printing company s employee salaries in dollars are recorded in the table below a For the data shown above find the following Round the answer in the first blank to 1 decimal place s In the second blank put the correct units Find the mean Find the median Find the range Salary 58456 90090 272500 52718 64553 74235 109739 66346 98837 57380 65270 73877 76029 108448 100702 Find the standard deviation

To construction a free body diagram first Select Select Select then and last

Which of the following is NOT a mechanism or process of evolution O genetic drift natural selection O drifting reproduction gene flow

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 403 gram setting Is there sufficient evidence at the 0 05 level that the bags are underfilled Assume the population is normally distributed State the null and alternative hypotheses for the above scenario Answer Keypad 0 Ho Ha Tables Keypad Keyboard Shortcut

An engineer has designed a valve that will regulate water pressure on an automobile engine The valve was tested on 160 engines and the mean pressure was 7 9 lbs square inch Assume the variance is known to be 0 36 If the valve was designed to produce a mean pressure of 7 8 lbs square inch is there sufficient evidence at the 0 01 level that the valve performs above the specifications State the null and alternative hypotheses for the above scenario Answer Ho H Keypa Keyboard Shortc Tables

Abaseball pitcher s eamed run average ERA is A e i 9e i where e is the number of earned runs given up by the pitcher and i is the number of innings pitched Good pitchers have low ERAS Assume that e20 and i 0 are real numbers a During his best season a certain pitcher pitched a total of 237 innings and gave up just 36 earned runs What was his ERA b Determine the ERA of a relief pitcher who gives up 5 eamed runs in one third of an inning c Graph the level curve A e i 2 and describe the relationship between e and i in this case a The pitcher s ERA for the season was Round to two decimal places as needed b The relief pitcher s ERA was Round to two decimal places as needed c Graph the level curve A e i 2 Choose the correct graph below OA A 10 Q OB Ai 10 CHILE Q OC A 10 U O D A 10 Q O

10 points total For each of the statements below state True T or False F or pick the correct option Explain your answer in 1 2 sentences For every part below 1 point for correct assertion and 1 point for correct explanation a T F Ridge regression does not have a closed form solution F b T F If we have m values for a hyperparameter of a classifier and we use k fold cross validation for hyperparameter tuning then we train the classifier mk times from scratch T c T F Perceptron is a supervised learning method that minimizes for the 0 1 loss F d T F Consider a linear function basis o x 1 log r 2323 where x R There exists a closed form solution for minimizing the mean squared error for the hypothesis he x To x If True state the solution Otherwise give a justification T e Which of the following is a common method for preventing overfitting in machine learning A Increasing the complexity of the model B Decreasing the size of the training data set C Regularization D Using a simpler evaluation metric E None of the above

According to a Bureau of Labor Statistics a worker in the U S spends on average 528 minutes a day on the job Suppose the standard deviation of the time spent on the job is 44 minutes A sample of 64 workers have a mean time 531minutes What is n What is A What is A What is the standard deviation of the sample means A 0 A What is the probability that the sample mean be more than 531 minutes Round to 3 decimal places

The average amount of corn yield is normally distributed with a mean of 168 7 bushels of corn per acre with a standard deviation of 27 bushels of corn In an agricultural study 81 randomly selected acres were harvested What is the probability that the mean corn yield of these 81 acres is less than 165 bushels of corn Round your answer to 3 decimal places A Question 4 1 5 points Please upload an image of your scratch work for the prior problem This should include a sketch of the sampling distribution the bell curve as demonstrated in the lesson

Sampling Good and Bad 1 A farmer brings a juice company many crates of oranges each week A company inspector looks at 10 or from the top of each crate before deciding whether to buy all the oranges Explain why this sampling m is biased Is the proportion of damaged oranges int eh sample likely greater than or less than the propor all oranges in the crate that are damaged Sample Sar

Evaluate 110 4 1 5 305 3

Bonnie went to the grocery store to buy some soda pop She noticed that different brand s cans contained varying amounts of pop GatorDew cans contained 350 milliliters SweetCola came in 359 milliliter cans OkraCola was sold in 358 ml cans and SugarUp came in 345 ml cans What was the average size the four cans ml

Order of Operations Evaluate using the correct order of operations Use your graphing calculator to check your answer 6 x 3 x 8 2 26 27 3 6 x 5 TAR 64 3 1 3 2 8 2x6

Evaluate using the correct order of operations Use your graphing calculator to check your answer 7 7 4 3 x 10 5 4 6 2 x 8 24 8 x 6 2

Eight kids report how many hours of television they watched on the weekend Their results are recorded here 9 1 20 11 4 10 13 12 Find the mean 1 hours O 10 hours O 10 5 hours

Evaluate 298 1 1 3 30 3 5

Evaluate 6 6 6

Evaluate 3 18 9 4 3

The table below shows a student s quiz scores on four quizzes Scores 17 20 20 17 Find this student s mean quiz score

Find the value of the expression 12 3 6 3

Evaluate 6 10 5 2 22

Evaluate 2 1 2 4 2 1 2 4

Evaluate the following expression 15 6 14

Find the value of the expression 12 3 7 4

Find 5 3 7 3

Evaluate 2 3 6 1

the base year calculate a Food Price Index for 1928 and 1940 Average weekly wages for the years covered in the table were 6 rubles in 1913 14 rubles in 1928 and 83 rubles in 1940 Using the Food Price Indexes you have just calculated assess what happened to the real wages of Russian workers between 1913 and 1940 Food prices in Russia before and after the 1917 Revolution in rubles per kilogram except milk in liters and eggs in units Foodstuffs consumed weekly in Moscow in 1926 Black Bread Wheat flour Potatoes Beef Mutton Sugar Milk Butter Eggs Sunflower oil Quantity 2 46 kgs 0 79 kgs 3 04 kgs 0 92 kgs 0 17 kgs 0 45 kgs 1 24 ltrs 0 11 kgs 1 60 eggs 0 12 kgs Price 1913 0 07 0 12 0 05 0 46 0 34 0 34 0 11 1 15 0 13 0 15 Price 1928 0 08 0 22 0 09 0 87 0 79 0 62 0 06 2 43 0 20 0 53 Price 1940 0 85 2 90 1 20 12 00 14 00 3 80 2 10 17 50 0 85 15 65