Probability Questions and Answers

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

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

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

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

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

Evaluate 298 1 1 3 30 3 5

Evaluate 3 18 9 4 3

Evaluate 6 10 5 2 22

Evaluate the following expression 15 6 14

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

Score 0 38 0 12 answered Question 11 Suppose an investment account is opened with an intial deposit of 11 000 earning 9 3 interest Round all answers to the nearest dollar a How much will the account be worth after 30 years if it is compounded monthly Submit b How much will the account be worth after 30 years if it is compounded continuously Question Help VIDEO Written Example Post to forum

Mainline Produce Corporation acquired all the outstanding common stock of Iceberg Lettuce Corporation for 32 000 000 in cash The book values and fair values of Iceberg s assets and liabilities were as follows Current assets Property plant and equipment Other assets Current liabilities Long term liabilities Required Galculato Book Value 12 600 000 25 200 000 4 200 000 8 000 000 15 000 000 Fair Value 15 600 000 31 200 000 5 200 000 8 000 000 14 000 000

The ages a Assuming that 2 of the ages are randomly selected with replacement list the different possible samples OA 55 46 55 60 46 55 46 60 60 55 60 46 B 55 55 55 46 55 60 46 55 46 46 46 60 60 55 60 46 60 60 c 55 46 55 60 46 60 OD 55 55 55 46 55 60 46 46 46 60 60 60 b Find the range of each of the samples then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution Sample Range Probability 7

The ages years of three government officials when they died in office were 55 46 and 60 Complete parts a through d a Assuming that 2 of the ages are randomly selected with replacement list the different possible samples OA 55 46 55 60 46 55 46 60 60 55 60 46 OB 55 55 55 46 55 60 46 55 46 46 46 60 60 55 60 46 60 60 OC 55 46 55 60 46 60 OD 55 55 55 46 55 60 46 46 46 60 60 60

Cholesterol levels mg dL were collected from a random sample of patients two days after they had a heart attack A For the data shown above find the following Round the answer in the first box to 2 decimal places Put the correct units in the second box Find the mean Find the median Cholesterol level 280 206 142 276 234 160 224 226 310 220 318 270 210 294 272 244 288 236 282 288 Find the mode

the age of 30 to save for retirement you decide to deposit 50 at the end of each month in an IRA at pays 3 5 compounded monthly b Use the following formula to determine how much you will have in the IRA when you retire at age 65 A A P 1 0 1 T A E nt Find the interest or his que poin s possible in the IRA when you retire a You will have approximately Do not round until the final answer Then round to the nearest dollar as needed b The interest is approximately Use the answer from part a to find this answer Round to the nearest dollar as needed

OBFW Publishers How well do professional golfers putt from different distances Researchers collected data on the percent of putts made for various distances to the hole in feet Residual 02 0 0 02 0 4 3 0 33 40 Predicted In percent made Starnes Tabor The Practice of Statistics 6e 0 2018 Bedford Freeman Worth High School Publishers 25 In percent made Model In percent made vs Distance Predictor Coef Constant Distance S 0 160 4 6649 percent made 0 1091 R sq 0 939 SE Coef 0 0825 0 0067 Calculate and interpret the residual for the point where the golfers made 31 of putts from 14 feet away Enter all calculations below accurate to at least 2 decimal places T 56 511 16 24 R Sq adj 0 936 P 0 0000 0 0000

An industrial engineer conjectures that a major difference between successful and unsuccessful companies is the percentage of their manufactured products returned because of defectives In a study to evaluate this conjecture the engineer surveyed the quality control departments of 50 successful companies identified by the annual profit statement and 50 unsuccessful companies The companies in the study all produced products of a similar nature and cost The percentages of the total output returned by customers in the previous year are provided in following table Unsuccessful 11 35 Businesses 8 34 6 56 8 93 8 26 Successful Businesses 10 24 5 43 5 09 3 62 4 06 9 19 7 69 6 85 7 32 7 07 6 16 6 32 8 20 2 23 7 70 10 30 13 58 8 06 13 70 12 23 5 06 0 43 10 51 1 08 8 32 8 59 10 49 7 71 8 67 11 93 10 64 7 30 1 94 9 16 6 33 4 98 11 07 11 04 10 08 4 76 Unsuccessful Successful 6 77 0 47 9 82 6 07 3 83 6 82 6 98 11 69 8 53 13 81 10 13 10 82 6 69 7 51 4 96 6 03 9 77 9 40 9 14 11 41 4 59 9 34 0 91 4 46 9 05 The sample means and standard deviations are N Mean 50 8 97 50 5 72 11 15 9 36 10 00 9 02 6 44 1 38 2 39 6 17 2 13 6 41 9 38 8 39 5 45 6 70 9 50 8 81 11 06 0 17 2 41 0 27 8 32 7 98 9 67 5 66 8 99 1 97 4 19 7 47 7 24 8 48 St Dev 2 20 3 24 Let u mean percentage of their manufactured products returned because of defectives from unsuccessful

Evaluate on your calculator 63 Give your answer rounded to two decimal places

What is the largest perfect square factor of 8 Simplify 8 completely to the form av

Evaluate each expression using order of operations A 3 B 3 Do you notice a pattern in your answers

Simplify 44 04 11 011 4 011 2 02 11

Simplify 180

Find the square root 49

11 Men s Heights The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2 5 inches Use the Empirical Rule to answer the following questions a What percent of men are taller than 74 inches b Between what heights do the middle 95 of men fall c What percent of men are between 64 and 66 5 inches tall d A height of 71 5 inches corresponds to what percentile of adult male American heights

Multiple Choice Fill in the correct answer to each of the following questions on the scantron form 2 pts each 1 In the NUSAP system for quantitative data presentation the S stands for A Statistics B Standard Deviation C Spread D Significant Figures 2 In NUSAP this factor encompasses everything done to stand behind the data s reliability Qa Qc traceability of weights etc A N B U C S D A E P 3 In statistics the null hypothesis Ho usually is stated as Wha A There is a significant difference between 2 values unless proven otherwise B There is no way of knowing for certain if 2 values are different C There is no statistically significant difference between 2 values D The difference between 2 values decreases as their uncertainties increase 4 Which test can be used to determine if there is an outlier in a set of data A Dixon B Q C Grubbs D All of the above 5 When would a one tailed table be used to determine if an outlier can be statistically excluded 12 A If the data does not follow a gaussian distribution rawalbe B If the outlier always falls to one side of the curve C If the data point doesn t look right D Never 6 A laboratory must be and an individual analyst should be do demonstrate their qualifications A certified also certified B accredited also accredited C certified accredited

4 2 pts A group of students recorded the colors of all of the cars in a parking lot Their results are show to the right a How many cars were there b What is the relative frequency of the green cars 12 10 8 6 4 2 0 white silver Number of cars dt red blue black green gray

2 2 pts The distribution to the right shows the heights of black cherry trees a What is the class bucket width of this distribution b How many black cherry trees are between 75 and 85 feet tall 8 Frequency 4 2 0 Heights of Black Cherry Trees 60 65 75 80 85 90 70 Height feet

6 1 pt Convert 48 to a simplified fraction

3 10 2023 Level 1 5 cm B 10 2023 Level 2 7 5 cm B 10 2023 Level 3 12 cm 3 10 2023 Level 4 15 cm 3 16 2023 Level 1 5 cm 3 16 2023 Level 2 7 5 cm 3 16 2023 Level 3 12 cm B 16 2023 Level 4 15 cm B3 20 2023 Level 1 5 cm 3 20 2023 Level 2 7 5 cm 8 20 2023 Level 3 12 cm 17 22 18 15 11 15 20 16 5 11

The pie chart to the right shows how adults rate their financial shape Suppose 4 people are chosen at random from a group of 1300 What is the probability that all four would rate their financial shape as excellent Make the assumption that the 1300 people are represented by the pie chart The probability is Round to six decimal places as needed Excellent 7 Good 44 Fair 35 Poor 13 Other 1 www

A 23 22 A A A 19 4 IN 3238 34 2A 23 INN A2 23 WIM 163 DA 4 4 A 44 49954 a fa 5 55 S 71 516 10 18 1995 6 pts For the following questions we are considering a standard deck of cards I have included an image for your reference What is the probability that we will draw a face card

The contingency table below categorizes the passengers who survived the Titanic disaster based on the class of ticket they purchased and their gender Class Female Male Total 1st 191 2nd 118 3rd 139 Total 448 133 58 94 24 81 58 308 140 Suppose one passenger is picked at random from the survivors Give the probability of each event rounded to four decimal places a Find the probability that a survivor is male 3125 b What is the probability that a survivor was in the 1st class OF 4263 c What is the probability that a survivor was a male or in the 1st class d What is the probability that a survivor was a male and in the 1st class e What is the probability that a survivor was a male given that the person was in 1st class

A NA N 4 14 N4 40 Me 4 103 4 ne MA 4 45 4 SE 26 0 69 As shown above a classic deck of cards is made up of 52 cards 26 are black 26 are red Each color is split into two suits of 13 cards each clubs and spades are black and hearts and diamonds are red Each suit is split into 13 individual cards Ace 2 10 Jack Queen and King Leave answers as reduced fractions a If a card is randomly selected what is the probability of drawing a n 9 of one suit 1 13 X

jar contains 5 red marbles 2 white marbles and 6 blue marbles Two marbles are randomly selected from he jar with replacement Find the following probabilities Leave your answer as a reduced fraction a A red marble and then a blue marble is randomly selected b A white marble and then a red marble is randomly selected

A jar contains 4 red marbles numbered 1 to 4 and 10 blue marbles numbered 1 to 10 A marble is drawn at random from the jar Round your answer to four decimal places Find the probability that the a marble is red b marble is odd numbered c marble is red or blue

40 of all shoes sold are purchased online 10 of all shoes sold are returned and 4 of all shoes sold are both purchased online and returned a Find the probability that a pair of shoes is returned given that the shoes were purchased online You can solve this problem using a Venn diagram or with a formula Round to two decimal places as necessary b Are the events shoes purchased online and shoes returned independent Justify your answer with probability O The events are independent because the chance that shoes are returned is different once it is known they were purchased online O The events are not independent the chance that shoes are returned is different once it is known they were purchased online The events are independent because the chance that shoes are returned stays the same once it is known they were purchased online The events are not independent because the chance that shoes are returned stays the same once it is known they were purchased online

A coin is flipped and die is rolled once What is the probability of flipping a heads on the coin and rolling a 5 on the die Give your answer as a reduced fraction

Suppose you flip two coins What is the probability of getting at most one heads Give your answer as a reduced fraction

A die is rolled twice What is the probability rolling a 5 first followed by rolling an even number Leave you answer as a reduced fraction

One card is randomly selected from a standard deck of 52 cards What is the probability of randomly selecting a n Jack or Ace Enter your answer as a reduced fraction

Maloree has asked her friends whether they prefer bacon or sausage She has recorded her results in the table below Sausage 20 16 36 Now that she s looking at the data she wonders if preferring sausage is independent of being female Use the data in the table to answer the questions Male Female Total Bacon 7 19 26 a P sausage b P sausage female Total 27 35 62 Round to four decimal places as necessary Round to four decimal places as necessary

The following data represent the number of different communication activities used by a random sample of teenagers in a given week Complete parts a through d Activities Male Female Total 0 21 21 42 1 2 3 4 5 81 53 134 58 40 56 70 114 110 Total 200 200 400 2X41 a Are the events female and 0 activities independent

Suppose that E and F are two events and that N E and F 250 and N E 500 What is P FIE P FIE Round to three decimal places as needed

uppose that E and F are two events and that P E and F 0 3 and P E 0 8 What is P FIE Tupo an integer or a decimal

Suppose that E and F are two events and that N E and F 330 and N E 510 What is P FIE www P FIE Round to three decimal places as needed

The probability that a randomly selected individual in a country earns more than 75 000 per year is 7 5 The probability that a randomly selected individual in the country earns more than 75 000 per year given that the individual has earned a bachelor s degree is 7 5 Are the events earn more than 75 000 per year and earne a bachelor s degree independent Are these events independent O No Yor