Probability Questions and Answers

5 3 OB 51 Which of the following cannot be a O A Question

Question 4 of 22 Identify the sample space of the probability experiment and Draw a tree diagram Determining a person s favorite steak rib eye R filet rare R medium M well done W

The average number of words in a romance novel is 64 416 and the standard deviation is 17 277 Assume the distribution is normal Let X be the number of words in a randomly selected romance novel Round all answers to 4 decimal places where possible a What is the distribution of X X N 64 416 b Find the proportion of all novels that are between 67 871 and 81 693 words c The 70th percentile for novels is 17 277 d The middle 70 of romance novels have from Round to the nearest word words Round to the nearest word words to words

8 Total 4 Marks The time it takes to vote may affect the outcome of an election For example some people may decide not to vote in districts with long lines and delays The mean time to vote in the 2012 election was approximately 14 minutes and Florida voters had the longest wait Suppose the time to vote for a randomly selected person in Florida X has a uniform distribution between 10 and 60 minutes Find the time t such that 75 of all people have to wait at most t minutes to vote

Q17 An insurance company charges 500 for an insurance policy against fire and theft in the home If a home is destroyed by fire then the insurance company will pay the homeowner 250 000 What is the expected value per policy to the insurance company if the probability that a home will be destroyed by fire is 0 0003 B 424 85 X A 425 00 Q18 You roll a standard die once 1 2 3 4 5 6 A is the event that you roll a prime number What is the probability of AC the complement of A A 1 3 B 2 3 C 1 6 C 412 85 D 510 12 0 0 01 D 1 2 Q19 We choose a household at random and X number of TVs in the house We have the following 3 0 01 0 1210 x 2 1 2 E Chocolate Cake 0 55 E O D 2 0 30 4 P X 0 12 What is the probability that a randomly selected household has no more than two TVs A 0 68 B 0 87 C 0 55 D 0 85 E 0 32 Q20 The mean of X is 5 and the standard deviation of X is 1 The variable X is transformed according to the formula Y 2X 1 What is the standard deviation of Y A 9 B 1 C 1 E 2 0 02

The amounts in dollars paid by students for textbooks during the fall term are given below 21 54 29 35 28 45 25 31 64 61 24 58 61 39 45 51 28 33 65 39 Fill in the correct frequencies in the frequency table based on the data Interval Frequency 10 19 99 Frequency of Cost 20 29 99 30 39 99 40 49 99 50 59 99 60 69 99 10 20 30 40 50 Cost 60 70 Does the histogram above represent this data 2 80

The scores of 50 students are given below 74 76 109 49 114 129 154 138 34 24 142 20 71 102 106 64 32 106 41 78 81 38 71 86 64 55 146 141 135 134 71 57 120 102 83 123 134 109 74 131 128 140 97 67 95 38 57 120 79 151 a Construct a frequency distribution for the data Use 20 39 for the first class and use 20 for the class width for each subsequent class Class Frequency 20 39

Please read over the following scenario Then choose an answer that best describes why the scenario is not a binomial probability distribution In a survey 110 adults were randomly selected Each adult was asked if they have one or more credit cards When these adults were randomly selected 67 had one or more credit cards The scenario is a binomial probability distribution The probability of success in one trial needs to be fixed There needs to be another outcome in order for this scenario to result in a binomial probability distribution As is the trials are not independent

We learned that with every discrete probability distribution there are two ways to determine if x successes is considered a significantly high number or a significantly low number One way is to calculate the mean and the standard deviation to determine the range rule of thumb The other way is to find the probability of P x and compare it with 0 05

In analyzing hits by V 1 buzz bombs in WWII South London was partitioned into 576 regions each with an area of 0 25 km A total of 535 bombs hit the combined area of 576 regions The mean number of hits per region is 0 929 Find the probability that a randomly selected region had exactly 2 hits Round your answer to 4 significant figures The probability that a randomly selected region had exactly 2 hits is

Question 8 Professor Sharpwit has 60 students in her Adva of them are Basket Weaving majors While gues Basket Weaving PBW class also taken exclusiv scans through all of the Zoom windows and reco enrolled in ABW Hmm Sharpwit muses ther but I think I can estimate approximately how ma

stion 6 oln Petersen models ar first survey M the nur

6 4 8 3 Boxplot Annual Mileage 11 2 15 4 thousand miles at is the maximum number of miles reported 10 15 Thousands of Miles Driven Annually esearcher surveyed 386 adults and recorded the number of miles they drove their car in one year e results are in the boxplot above and the annual number of miles is measured in 1000 s at is the range of the data values thousand miles enty five percent of the data are above what value thousand miles venty five percent of the data are above what value thousand miles at percent of the data values are between 8 3 and 24 7 24 7 20 25

In a study the sample is chosen by surveying every 3rd driver coming through a tollboot What is the sampling method Simple Random Convenience Stratified Systematic Cluster

In a study the data you collect is favorite candy bar This data is O Quantitative Discrete Quantitative Continuous O Qualitative Categorical

istics SP1 2023 K Results of a 2017 survey of a sample of executives from 154 banks reveal insights on banking priorities a importance is boosting profitability and identifying growth areas Fifty two percent of bank institutions note mobile app relationship management MARM solution was ranked as the top most important omnichanne greatest anticipated strategy to enhance the customer experience Complete parts a through d MINIME Question 19 of 20 OA the 55 bank institutions in the region that cite mobile app banking enhancements as the greatest a OB the 154 executives representing bank institutions OC the 55 bank institutions in the OD the 80 bank institutions in the rec that note mobile app experience initiatives as an area in whi OE all bank executives PA c What is a possible parameter of interest

t Final Exam n list 5 6 K The accompanying table contains the service ratings of 14 different Interne BEE Click the icon to view the data table O A Boxplot 40 Difference Que JOU O Does the assumption needed in order to conduct the t test in a appear to OA No the boxplot is approximately symmetric B Yes the boxplot is approximately symmetric OC Yes the boxplot indicates skewness OD No the boxplot indicates skewness

1800 Business Statistics SP1 2023 st Final Exam on list ion 11 n 12 13 4 K Results of a 2017 survey of a sample of executives from 154 banks re importance is boosting profitability and identifying growth areas Fifty t mobile app relationship management MARM solution was ranked as greatest anticipated strategy to enhance the customer experience Co OA the 55 bank institutions in the region that cite mobile app bank OB the 154 executives representing bank institutions OC the 55 bank institutions in the region O D the 80 bank institutions in the region that note mobile app expe OE all bank executives c What is a possible parameter of interest OA the proportion of bank institutions in the region that cite mobile

5 What is the relationship between educational achievement and home ownership A random sample of 500 U S adults was selected Each member of the sample was identified as a high school graduate or not and as a homeowner or not The way way table summarizes the data High school graduate Yes No 221 119 89 71 Homeowner Yes No a Suppose we choose 1 member of the sample at random Are the events homeowner and high school graduate independent Justify your answer

4 A survey of all residents in a large apartment complex reveals that 68 use Faceb both Suppose we select a resident at random CO26 877 a Make a two way table to display the sample space of this random process Shinobuz SKANDT Facebook Instagram PT p an 917 evue betaubfed tand the visluger neblinks vnam word Sidst vew owi srl ni nwode 916 616b gnitlu291 9T 1ebne elsme ott 20Y aar OET on 203 ars OSS HOT b Find the probability that the person uses neither Facebook nor Instagram Brilis 26 81 16 1n9bu12 9l6mal 6 gnittag 26 Jngv9 9n tsd mobn61 ds lo OOE 200 selain FACEBOO elsM oet VEDY HOLs thob anw c Use your two way table from part a to make a Venn diagram of the sample spad INSTAGRA C Vide 1x910 on me

Finding probabilities of events and complements In a certain online computer game there are 440 players on the Green Team and 1000 players total in the game The game randomly chooses a player to receive a bonus Let the event A and the event B be as follows A The player the game chooses is on the Green Team B The player the game chooses is not on the Green Team Find the following probabilities Write your answers as decimal numbers and do not round P A 0 44 P B X

Due to a manufacturing error three cans of regular soda were accidentally filled with diet soda and placed into a 18 pack Suppose that two cans are randomly selected from the 18 pack Complete parts a through b

Refer to the table summarizing service times second dinners at a fast food restaurant How many individ included in the summary Is it possible to identify the values of all of the original service times individuals are included in the summary e a whole number ossible to identify the exact values of all of the No The frequency distribution tells nothing

Given f x kx2 0 find f x 0 elsewhere find the value of k for which f x is valid density function Find P 1

6 You have been playing a certain jackpot game the game 499 times and have yet to win but your worst enemy who lives around the corner from you played only once and won Which of the following is true there maybe more than one statement true or even none Explain each answer A The modeled probability of winning the game is 1 500 B The relative frequency of winning the game is 1 500 C The relative frequency that you will win the game is zero D The relative frequency of winning the game is greater than the modeled probability Solution

3 The following is a detail of an altered version of a painting by the artist Gene Davis This picture has been generated by the following rule There are a total of 24 vertical stripes on a black background consisting of four patterns in each of which you have three vertical grey stripes followed by three closely spaced stripes of different colors Each colored stripe can be teal light blue dark blue lilac yellow or maroon so long as no color repeats in any group of three You were planning to open a huge gallery showing every possible painting satisfying this rule but your sponsors refused to go ahead because of the sheer size of the gallery you would need so you eliminated all paintings that had orange or light blue stripes and were allowed to go ahead with the smaller collection In the grand opening a photographer takes a picture of one of the paintings at random What is the probability that it is the very picture shown above Solution

5 A covid 19 test manufacturer is testing its newest instant test It tests a total of 500 people 100 of whom are known to have the virus The following table shows the results Test is positive T Test is negative T Total Have virus V 90 30 120 Do not have virus V 40 160 200 Total a Find the probability that a person has the virus but tests negative b Find the probability that a person who has the virus tests negative 130 190 320 c Find the probability that a person who tests negative has the virus d An acquaintance of yours has a negative test result What is the probability that she does not have the virus Solution

mpling Question 12 1 Determine whether the variable is qualitati Colors of marbles drawn from an urn The variable is because col

ampling jn Question 13 1 2 17 The jersey numbers for players on a hockey team are liste 5 13 10 41 Identify the level of measurement of the data set Explain v 7 31 20 26 49 21 16 29

ling Question 17 1 3 2 What is the difference between a census and a Choose the corro

ampling In Question 9 1 1 49 Part 1 of 4 In a recent study on the effects of sleep and tes of sleep were three times more likely to answer volunteers Complete parts a through d

impling 1 Question 7 1 Part 1 of 2 Suppose a survey of 953 business owne the descriptive branch of statistics Mak

ample V Question 13 8 2 11 T Part 1 of 4 est the claim about the difference between two population means and andom and independent and the populations are normally distributed laim H H 0 10 Assume o2 02 ample statistics x 2408 s 180 n 12 and x 2310 S 52 n 10 entify the null and alternative hypotheses Choose the correct answer b

mple Question 17 8 3 at conditions are necessary in order to use the de ose the correct answer below

ple Question 5 8 1 9 he technology display to make a decision to reject or dardized test statistic and using the P value Assume Click the icon to view the technology display

estion 15 udy conducted at a large state university involved 435 gradua ses and their majors are summarized in the table below Program Accounting 30 Grade of A Table of ma Gra 40

try 3 of 4 pts See Details for more this question below 3 4 P cts a total of 371 people Of these 74 people were in the 18 21 age b them respond to her poll while 36 refuse to respond The other 297 p Of these 278 respond and 19 refuse to respond one of the 371 people is randomly selected Find the probability of go et Round to 3 decimal places bability of getting someone in the 18 21 age bracket AND who refused es bability of getting someone who refused to respond Round to 3 decima

uestion 22

h8 ed You have two die calcula First set up the sample s

ents S Question 29 The following results are provided from a tes where a negative test is Event A complement error So actual marijuana use is Event B and 144 subjects tested positive and 154 tested negatives meaning they actually had used m positives meaning they had actually not use a How many subjects were included in the

Question 28 In a hospital unit there are 8 nur females Create a contingency table of nu a If a staff person is randomly s

Question 30 In your music collection 75 are bur player in your car is very particular realized your car CD player will play Let event Boccur if the

On the Trends in International Math and Science Study test in a recent year the U S scored an average of 508 Suppose that we take a random sample of n U S scores and that the population standard deviation is 72 If the probability that the mean of the sample exceeds 520 is 0985 what was the sample size Round to the nearest 1 Sample Size Plank 14

In statistics Baye s Theorem is used to calculate O relative frequency probability O classical probability O marginal probability conditional probability

A statistical experiment is a process that when performed O results in exactly one of many possible observations results in at least two of many possible observations may not lead to the occurrence of any outcome O results in exactly one of two possible observations O

Which of the following is not an example of a discrete random variable O The number students in each class at a college The time spend studying for an exam O The amount of runs scored in a baseball game O The number of graduates each semester

There are 7 beads in a bowl There is a number on each bead 1 4 4 5 7 Olly takes at random three of the beads He works out the sum of the numbers on the three beads Work out the probability that the sum is an odd number

Studies show that 5 of all credit card holders eventually become delinquent Determine the probability that exactly 6 people out of a random sample of 18 people will eventually become delinquent Use the Binomial probability formula or the binomial probability table if possible to solve O 0 6493 O 0 1654 00 4815

A study found that 50 of Americans do not have adequate retirement savings Determine the probability that at least 1 person out of a random sample of 9 Americans does not have adequate retirement savings Use the Binomial probability formula or the binomial probability table if possible to solve O 0 9102 O0 5169 0 0176 0 998

O contains one or more of the outcomes of an experiment contains all possible outcomes of an experiment O contains exactly one of the outcomes of an experiment O contains two or more of the outcomes of an experiment