Probability Questions and Answers

Suppose that E and F are two events and that P E and F 0 3 and P E 0 8 What is P FIE P FE Type an integer or a decimal

The notation P F E means the probability of event given event

5 39 A consumer testing agency wants to evaluate the claim made by a manufacturer of discount tires The manufacturer claims that its tires can be driven at least 35 000 miles before wearing out To determine the average number of miles that can be obtained from the manufacturer s tires the agency randomly selects 60 tires from the manufacturer s warehouse and places the tires on 15 cars driven by test drivers on a 2 mile oval track The number of miles driven in thousands of miles until the tires are determined to be worn out is given in the following table Car 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ny S Miles Driven 25 27 35 42 28 37 40 31 29 33 30 26 31 28 30 15 31 47 5 04 a Place a 99 confidence interval on the average number of miles driven prior to the tires wearing out b Is there significant evidence a 01 that the manufacturer s claim is false What is the level of significance of your test Interpret your findings

5 36 The ability to read rapidly and simultaneously maintain a high level of comprehension is often a determining factor in the academic success of many high school students A school district is considering a supplemental reading program for incoming freshmen Prior to implementing the program the school runs a pilot program on a random sample of n 20 students The students were thoroughly tested to determine reading speed and reading comprehension Based on a fixed length standardized test reading passage the following reading times in minutes and comprehension scores based on a 100 point scale were recorded

Recognize the importance of accounting ethics and interperso resolving accounting issues analyze record and report financial information for a service business using Interpret and apply Generally Accepted Accounting Principles GAAP to computerization Evaluate a complete accounting cycle including the analysis and recording process through post closing trial balance for a service business using computerization Directions Using the information below put the transactions in pro forma and complete the required journal entries posting and check your work with a trial balance Use this Word document OR the Excel template provided in Blackboard 10 transactions 5 pts each 20 general ledger postings 1 5 pts each and Trial Balance 20 pts total 12 Mar 1 Mar The owner of KJO Withholdings invested 75 000 cash into the company 2 Mar The company purchased 2 725 worth of supplies on account 5 Mar The company purchased equipment worth 5 700 on the account Paid 24 months of insurance in advance for 4 500 cash 15 Mar Received 8 525 cash for services rendered to WBR Inc 17 Mar The company billed D T Automotive 5 520 for services rendered 20 Mar Received a down payment of 3 570 cash for work to be performed next from WBR Inc 25 Mar The owner withdrew 2 000 for personal use

5 2 In the research study on percentage of calories from fat a What is the population of interest b What dietary variables other than PCF might affect a person s health c What characteristics of the nurses other than dietary intake might be importan studying their health condition d Describe a method for randomly selecting which nurses participate in the study e State several hypotheses that may be of interest to the researchers

A geneticist conducts an experiment with beans one sample of offspring consisted of 461 green beans and 168 yellow beans Based on these results estimate the probability of getting an offspring bean that is green Report the answer as a percent rounded to one decimal place accuracy You need not enter the symbol 1 prob

On a 5 question multiple choice test where each question has 5 answers what would be the probability of getting at least one question wrong Give your answer as a fraction

If one card is randomly selected from a well shuffled standard deck of 52 cards what is the probability that the card selected is a 5 Leave your answer as a reduced fraction

14 41 off 3 S NO ND off me 108 34 ne e re k 4 4 4 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 b If a card is randomly selected what is the probability of drawing club or heart c If a card is randomly selected what is the probability of drawing a number smaller than 7 counting the ace as a 1

A die is rolled once Find the probabilities of the given events Leave your answer as a reduced fraction a The number rolled is a 3 b The number showing is an even number c The number showing is greater than 3

A group of people were asked whether they owned a dog The number of people that owned a dog was 158 and 186 responded that they didn t own a dog Find the probability that if a person is chosen at random he she own a dog Round your answer to two decimal places

A couple are each carriers for sickle cell disease a recessive condition What is the probability that this couple will have 2 children with sickle cell and one child without the disease 1 64 3 64 9 64

A friend wants to have four children What is the probability that she will have 3 girls and 1 boy 1 16 1 8 4 16 1 2

Fill in the blank Two events E and F are probability of event F Two events E and F are ility of ovent F if the occurrence of event E in a probability experiment does not affect the if the occurrence of event E in a probability experiment does not affect the

Rule

The following notes may be used for Population mean sigma know 9 2 Reject HO if X In X Za12 Zal2 n Test Statistic Z x o ol n Left tail Reject H0 when Right tail Reject H0 when Two tail Reject H0 when P value left tail p value P Z z right tail p value P Z Z two tail p value P Z z P Z Z Reject HO when O n Population Proportion 9 4 p Za12 Reject HO if Test Statistic P 1 P n 3 Z p Za12 P 1 P n p P 1 P TP

6 Using the frequency distribution below determine the class width Weight lbs 101 120 121 140 141 160 161 180 181 200 Answer Frequency 2 8 10 11 6 Previous Answer 37 W

Listeria monocytogenes is a Gram positive bacterium that can cause a life threatening illness termed listeriosis This foodborne pathogen is especially dangerous if consumed by high risk groups that include the elderly people with weakened immune systems pregnant women and newborns In the U S each year there is estimated to be 1 600 cases of listeriosis with 260 deaths Unfortunately L monocytogenes outbreaks are not uncommon and so far this year there have already been two The first outbreak which affected 19 individuals 18 of which required hospitalization was associated with the consumption of leafy greens This outbreak spanned 16 states and included a case in Oklahoma The second outbreak which is still considered active involves the recall of contaminated Soft Serve On The Go ice cream cups with an individual in NY and PA both requiring hospitalization Knowing that L monocytogenes has a doubling time of 45 minutes and that ingestion of 1 x 10 bacteria can cause disease in high risk group members what would be the effect i e illness or not if an elderly resident of an assisted living facility consumed several pieces of lunch meat that originally contained a total of 7 631 organisms but which had been sitting in an improperly refrigerated deli display case for 3 hours which allowed optimal growth of the bacteria To justify your answer i e illness or not show all work use scientific notation in the format a aa x 10 and make sure to include the appropriate units 3 pts

Which of the following graphs corresponds to the following set 1 0 O 4 3 2 1 0 O 4 3 2 1 0 4 O 1 4 3 2 1 0 1 3 2 1 F O 1 2 0 1 2 2 2 3 3 4 3 Pat 3 4 4

Graph each inequality and then give interval notation entry tip use two o s as in octopus for infinity oo for ao and oo for o x 3 5 4 3 2 1 0 Clear All Draw x 2 Interval notation for the above inequality and graph is 5 4 3 2 1 0 2 3 Clear All Draw O 2 O 3 4 Interval notation for the above inequality and graph is

Graph the inequality 3 or 1 x 2 6 5 4 3 2 1 0 1 2 3 4 5 6 Clear All Draw

Which of the following choices corresponds to the graph 3 2 O 1 0 1 2 3 1 1 1 1 00

The accompanying table describes probabilities for the California Daily 4 lottery The player selects four digits with repetition allowed and the random variable x is the number of digits that match those in the same order that they are drawn for a straight bet Use the range rule of thumb to determine whether 4 matches is a significantly high number of matches Select the correct choice below and if necessary fill in the answer box within your choice O A Significantly high numbers of matches are significantly high number of matches Round to one decimal place as needed OB Significantly high numbers of matches are significantly high number of matches Round to one decimal place as needed OC Significantly high numbers of matches are significantly high number of matches Round to one decimal place as needed CUE OD Significantly high numbers of matches are significantly high number of matches Round to one decimal place as needed OE Not enough information is given X 0 1 2 3 4 or more Since 4 is less than this value 4 matches is not a P x 0 659 0 294 0 044 0 004 0 or less Since 4 is at least as low as this value 4 matches is a or less Since 4 is greater than this value 4 matches is not a or more Since 4 is at least as high as this value 4 matches is a

Express the set x 2 using interval notation

Express the set 8 x 9 using interval notation

Refer to the accompanying table which describes the number of adults in groups of five who reported sleepwalking Finc the mean and standard deviation for the numbers of sleepwalkers in groups of five Click the icon to view the data table The mean is sleepwalker s Round to one decimal place as needed Table of numbers of sleepwalkers and probabilities X012345 P x 0 163 0 369 0 297 0 132 0 035 0 004 X

Based on a survey when 1009 consumers were asked if they are comfortable with drones delivering their purchases 42 said yes The probability of randomly selecting 30 of the 1009 consumers and getting exactly 24 who are comfortable with the drones is represented as 0 What does 0 indicate Does 0 indicate that it is impossible to get exactly 24 consumers who are comfortable with drones Choose the correct answer below OA The probability 0 indicates that the probability is a very small positive value It indicates that the event is impossible OB The probability 0 indicates that the probability is zero It indicates that the event is impossible OC The probability 0 indicates that the probability is a very small positive value It indicates that the event is likely OD The probability 0 indicates that the probability is a very small positive value It indicates that the event is possible but very unlikely

A Gallup poll of 1236 adults showed that 12 of the respondents believe that it is bad luck to walk under a ladder Consider the probability that among 30 randomly selected people from the 1236 who were polled there are at least 2 who have that belief Given that the subjects surveyed were selected without replacement the events are not independent Can the probability be found by using the binomial probability formula Why or why not Choose the correct answer below OA Yes There are a fixed number of selections that are independent can be classified into two categories and the probability of success remains the same OB Yes Although the selections are not independent they can be treated as being independent by applying the 5 guideline OC No The selections are not independent and the 5 guideline is not met D No The selections are not independent

Multiple choice questions each have five possible answers a b c d e one of which is correct Assume that you guess the answers to three such questions a Use the multiplication rule to find P CWC where C denotes a correct answer and W denotes a wrong answer P CWC Type an exact answer

Based on a survey assume that 54 of consumers are comfortable having drones deliver their purchases Suppose we want to find the probability that when five consumers are randomly selected exactly three of them are comfortable with the drones What is wrong with using the multiplication rule to find the probability of getting three consumers comfortable with drones followed by two consumers not comfortable as in this calculation 0 54 0 54 0 54 0 46 0 46 0 0333 Choose the correct answer below OA The probability of the second consumer being comfortable with drones cannot be treated as being independent of the probability of the first consumer being comfortable with drones OB The calculation assumes that the first three consumers are comfortable with drones and the last two are not but this arrangement is not possible OC There are other arrangements consisting of three consumers who are comfortable and two who are not The probabilities corresponding to those other arrangements should also be included in the result OD The event that a consumer is comfortable with drones is not mutually exclusive with the event that a consumer is not comfortable with drones

There is a 0 9985 probability that a randomly selected 33 year old male lives through the year A life insurance company charges 199 for insuring that the male will live through the year If the male does not survive the year the policy pays out 120 000 as a death benefit Complete parts a through c below a From the perspective of the 33 year old male what are the monetary values corresponding to the two events of surviving the year and not surviving The value corresponding to surviving the year is The value corresponding to not surviving the year is Type integers or decimals Do not round b If the 33 year old male purchases the policy what is his expected value The expected value is Round to the nearest cent as needed c Can the insurance company expect to make a profit from many such policies Why because the insurance company expects to make an average ofit of on every 33 year old male it insures for 1 year Round to the nearest cent as needed

Based on a poll among adults who regret getting tattoos 19 say that they were too young when they got their tattoos Assume that nine adults who regret getting tattoos are randomly selected and find the indicated probability Complete parts a through d below a Find the probability that none of the selected adults say that they were too young to get tattoos Round to four decimal places as needed b Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos Round to four decimal places as needed 3 c Find the probability that the number of selected adults saying they were too young is 0 or 1 Round to four decimal places as needed d If we randomly select nine adults is 1 a significantly low number who say that they were too young to get tattoos because the probability that of the selected adults say that they were too young is 0 05

According to a poll about 16 of adults in a country bet on professional sports Data indicates that 47 1 of the adult population in this country is male Complete parts a through e OA Yes A person can be both male and bet on professional sports at the same time B No A person can be both male and bet on professional sports at the same time O C Yes A person cannot be both male and bet on professional sports at the same time OD No A person cannot be male and bet on professional sports at the same time b Assuming that betting is independent of gender compute the probability that an adult from this country selected at random is a male and bets on professional sports P male and bets on professional sports 0 0754 Type an integer or decimal rounded to four decimal places as needed c Using the result in part b compute the probability that an adult from this country selected at random is male or bets on professional sports P male or bets on professional sports 0 5556 Type an integer or decimal rounded to four decimal places as needed d The poll data indicated that 9 7 of adults in this country are males and bet on professional sports What does this indicate about the assumption in part b OA The assumption was correct and the events are independent OB The assumption was incorrect and the events are not independent

the problem The weights of certain machine components are normally distributed with a mean of 8 81 g and a standard deviation of 0 06 g Find the two weights that separate the top 3 and the bottom 3 These weights could serve as limits used to identify which components should be rejected O 8 70 g and 8 92 g O 8 68 g and 8 97 g O 8 78 g and 8 84 g 8 80 g and 8 82 g

Find the indicated probability In one region the September energy consumption levels for single family homes are four to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kV For a randomly selected home find the probability that the September energy consumpt level is between 1100 kWh and 1225 kWh O 0 3791 O 0 1971 O 0 0910 O 0 2881

Human body temperatures are normally distributed with a mean of 98 20 degrees F and a standard deviation of 0 62 degrees F If 19 people are randomly selected find the probability that their mean body temperature will be less than 98 50 degrees F O 0 0833 O 0 9826

For women aged 18 24 systolic blood pressures in mm Hg are normally distributed with a mean of 114 8 and a standard deviation of 13 1 If 23 women aged 18 24 are randomly selected find the probability that their mean systolic blood pressure is between 119 and 122 O 0 0577 O 0 3343 O 0 9341

If Z is a standard normal variable find the probability The probability that Z lies between 0 and 2 73 O 0 5032 O the answer is none of these choices O 0 9968

In airline applications failure of a component can result in catastrophe As a result many airline components utilize something called triple modular redundancy This means that a critical component has two backup components that may be utilized should the initial component fail Suppose a certain critical airline component has a probability of failure of 0 0056 and the system that utilizes the component is part of a triple modular redundancy a Assuming each component s failure success is independent of the others what is the probability all three components fail resulting in disaster for the flight b What is the probability at least one of the components does not fail a The probability is Round to eight decimal places as needed

The probability that a randomly selected 1 year old male feral cat will live to be 2 years old is 0 98037 a What is the probability that two randomly selected 1 year old male feral cats will live to be 2 years old b What is the probability that seven randomly selected 1 year old male feral cats will live to be 2 years old c What is the probability that at least one of seven randomly selected 1 year old male feral cats will not live to be 2 years old Would it be unusual if at least one of seven randomly selected 1 year old male feral cats did not live to be 2 years old a The probability that two randomly selected 1 year old male feral cats will live to be 2 years old is Round to five decimal places as needed

A random sample of 1953 adults was taken and they were asked if they prefer watching sports movies or news on tv They were also asked if they preferred dogs or cats Dog Cat Total Sports 371 148 519 Movies 524 138 662 News 480 292 772 Total 1375 578 1953 a What is the probability that a person selected at random likes dogs and movies b What is the probability that a person selected at random likes cats and news c What is the probability that a person selected at random likes dogs or movies d What is the probability that a person selected at random likes sports or cats

The answer above is NOT correct The shelf life of a batteries produced by one major company are normally distributed with a mean of 3 9 years and a standard deviation of 0 9 years The figure below shows the distribution of shelf lives of batteries produced by one major company Calculate the shaded area under the curve Express your answer in decimal form with at least two decimal place accuracy Answer 0004 3 297 4 8 Shelf Lives of Batteries Produced by One Major Company

College students average 8 2 hours of sleep per night with a standard deviation of 35 minutes If the amount of sleep is normally distributed what proportion of college students sleep for more than 9 3 hours Proportion 2 5 100

2 50 points eBook Karla Tanner opens a web consulting business called Linkworks and completes the following transactions in its first month of operations Prepare journal entries for each transaction and identify the financial statement impact of each entry The financial statements are automatically generated based on the journal entries recorded April 1 Tanner invested 80 000 cash along with office equipment valued at 26 000 in the company in exchange for common stock April 2 The company prepaid 9 000 cash for 12 months rent for office space The company s policy is to record prepaid expenses in balance sheet accounts April 3 The company made credit purchases for 8 000 in office equipment and 3 600 in office supplies Payment is due within 10 days April 6 The company completed services for a client and immediately received 4 000 cash April 9 The company completed a 6 000 project for a client who must pay within 30 days April 13 The company paid 11 600 cash to settle the account payable created April 3 April 19 The company paid 2 400 cash for the premium on a 12 month prepaid insurance policy The company s policy is to record prepaid expenses in balance sheet accounts April 22 The company received 4 400 cash as partial payment for the work completed on April 9 April 25 The company completed work for another client for 2 890 on credit April 28 The company paid 5 500 cash in dividends April 29 The company purchased 600 of additional office supplies on credit April 30 The company paid 435 cash for this month s utility bill Requirement General Journal General Ledger Trial Balance Income Statement St Retained Earnings Balance Sheet FS Impact General Journal Tab For each transaction prepare the required journal entry on the General Journal tab List debits before credits General Ledger Tab One of the advantages of general ledger software is that posting is done automatically To see the detail of all transactions that affect a specific account or the balance in an account at a specific point in time click on the General Ledger tab Check r

Find y if xy yx y

The number of children in seven families looked like this 0 3 4 9 1 1 2 Round all final answers to 2 decimal places a Q b Med

Are the following variables discrete or continuous a a person s age as listed on a driver s license discrete b the number of cars served at a fast food drive thru between noon and 2 pm continuo c The weights of elephants in captivity continuous

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level In an earlier study the population proportion was estimated to be 0 22 How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95 confidence level with an error of at most 0 037 Round your answer up to the next integer

At the local college a study found that students earned an average of 13 8 credit hours per semester A sample of 118 students was taken What is the best point estimate for the average number of credit hours per semester for all students at the local college 2 Daints Keypad