Statistics Questions

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

Suppose that E and F are two events and that P E 0 3 and P FIE 0 8 What is P E and F P E and F Simuli

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 30 A concern to public health officials is whether a concentration of lead in the paint of older homes may have an effect on the muscular development of young children In order to evaluate this phenomenon a researcher exposed 90 newly born mice to paint containing a specified amount of lead The number of Type 2 fibers in the skeletal muscle was determined 6 weeks after exposure The mean number of Type 2 fibers in the skeletal muscles of normal mice of this age is 21 7 The n 90 mice yielded y 18 8 s 15 3 Is there significant evidence in the data to support the hypothesis that the mean number of Type 2 fibers is different from 21 7 using an 05 test

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 16 A study is designed to test the hypotheses Ho 26 versus H 26 A random sample of 50 units was selected from a specified population and the measurements were summarized to y 25 9 and s 7 6 a With a 05 is there substantial evidence that the population mean is less than 26 b Calculate the probability of making a Type II error if the actual value of the population mean is at most 24 c If the sample size is doubled to 100 what is the probability of making a Type II error if the actual value of the population mean is at most 24

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

5 7 asic Inferences About for a Normal Population Unknown 5 34 Provide the rejection region based on a t test statistic for the following situation a Ho 28 versus H 28 with n 11 a 05 b Ho 28 versus Ha 28 versus Ha 28 versus Ha 28 with n 21 a 025 28 with n 8 a 001 c Ho d Ho 28 with n 13 a 01

5 1 The county government in a city that is dominated by a large state university is concerned that a small subset of its population has been overutilized in the selection of residents to serve on county court juries The county decides to determine the mean number of times that an adult resi dent of the county has been selected for jury duty during the past 5 years They will then compare the mean jury participation for full time students to that of nonstudents a Identify the populations of interest to the county officials b How might you select a sample of voters to gather this information

5 6 Refer to Exercise 5 5 The engineer in charge of the coffee manufacturing process examines the confidence intervals for the mean caffeine content calculated over the past several weeks and is concerned that the intervals are too wide to be of any practical use That is they are not provid ing a very precise estimate of a What would happen to the width of the confidence intervals if the level of confi dence of each interval is increased from 95 to 99 b What would happen to the width of the confidence intervals if the number of sam ples per hour was increased from 50 to 100

5 32 A tobacco company advertises that the average nicotine content of its cigarettes is at most 14 milligrams A consumer protection agency wants to determine whether the average nicotine content is in fact greater than 14 A random sample of 300 cigarettes of the company s brand yields an average nicotine content of 14 6 milligrams and a standard deviation of 3 8 milligrams Deter mine the level of significance of the statistical test of the agency s claim that is greater than 14 If a 01 is there significant evidence that the agency s claim has been supported by the data

5 33 A psychological experiment was conducted to investigate the length of time time delay between the administration of a stimulus and the observation of a specified reaction A random sample of 36 persons was subjected to the stimulus and the time delay was recorded The sample mean and standard deviation were 2 2 and 57 seconds respectively Is there significant evidence that the mean time delay for the hypothetical population of all persons who may be subjected to the stimulus differs from 1 6 seconds Use a 05 What is the level of significance of the test

5 14 The housing department in a large city monitors the rent for rent controlled apartments in the city The mayor wants an estimate of the average rent The housing department must deter mine the number of apartments to include in a survey in order to be able to estimate the average rent to within 100 using a 95 confidence interval From past surveys the monthly charge for rent controlled apartments ranged from 1 000 to 3 500 How many renters must be included in the survey to meet the requirements

5 7 Refer to Exercise 5 5 Because the company is sampling the coffee production process every our there are 720 confidence intervals for the mean caffeine content u constructed every month a If the level of confidence remains at 95 for the 720 confidence intervals in a given month how many of the confidence intervals would you expect to fail to contain the value of u and hence provide an incorrect estimation of the mean caf feine content b If the number of samples is increased from 50 to 100 each hour how many of the 95 confidence intervals would you expect to fail to contain the value of u in a given month c If the number of samples remains at 50 each hour but the level of confidence is increased from 95 to 99 for each of the intervals how many of the 99 confidence intervals would you expect to fail to contain the value of in a given month

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

2 Identify at least five issues that former Vice President Atiku brought against President Tinubu with regard to his university admission and Chicago university certificate at the Chicago USA court No more than 20 sentences 1 1171

An individual s income varies with age The table shows the median income I of individuals of different age groups within the United States for a certain year For each age group let the class midpoint represent the independent variable x For the class 65 years and older assume that the class midpoint is 69 5 Complete parts a through e A Quadratic with a 0 B Linear with positive slope c Quadratic with a 0 D Linear with negative slope Age 15 24 years 25 34 years 35 44 years 45 54 years 55 64 years 65 years and older Class Midpoint X 19 5 29 5 39 5 49 5 59 5 69 5 Median Income I 12 965 32 131 42 637 45 693 42 478 23 500 b Use a graphing utility to find the quadratic function of best fit that models the relation between age and median incon The quadratic function of best fit is y x x 0 Type integers or decimals rounded to three decimal places as needed

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 study is designed to test the hypotheses Ho 26 versus H 26 A random sample of 50 units was selected from a specified population and the measurements were summarized to y 25 9 and s 7 6 a With a 05 is there substantial evidence that the population mean is less than 26 b Calculate the probability of making a Type II error if the actual value of the population mean is at most 24 c If the sample size is doubled to 100 what is the probability of making a Type II error if the actual value of the population mean is at most 24

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

A random sample of 15 college students were asked How many hours per week typically do you work outside the home Their responses are shown on the right Determine the shape of the distribution of hours worked by drawing a frequency histogram and computing the mean and median Which measure of central tendency better describes hours worked Choose the correct frequency histogram below OA Hours Worked per Week Frequency ONA Oskewed left skewed right B Frequency ON A O mode O median www Hours Worked per Week 10 20 30 hours 10 20 30 hours Is the histogram for the data set skewed right skewed left or symmetric O symmetric Q O C Frequency 2 N A The mean number of hours worked by college students outside the home is approximately Type an integer or decimal rounded to three decimal places as needed The median number of hours worked by college students outside the home is Which measure of central tendency better describes hours worked hours 0 6 6 17 17 Hours Worked per Week 11 7 13 13 8 10 20 hours hours 30 11 15 25 11 C E

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

By measuring the absorbance readings of a set of McFarland standards construct a standard curve in Excel of bacterial cell concentration mL versus absorbance at 600 nm In addition Marco has applied linear regression analysis to their data to produce a trendline and an R value of the line of best fit see Marco s standard curve below Given these results if Marco measured an undiluted bacterial sample and obtained an absorbance reading of 0 17 what would be the expected bacterial cell concentration of that sample Show all work use scientific notation in the format a aa 10 and make sure to include the appropriate units 3 pts Marco s Standard Curve of Bacterial Concentration Versus Absorbance Average Absorbance at 600 nm 0 5 0 45 0 4 0 35 0 3 0 25 0 2 0 15 0 1 0 05 0 0 00E 00 2 00E 08 Mahar 04b l 4 00E 08 6 00E 08 Bacterial Cells mL 8 00E 08 y 3E 10x 0 0088 R 0 9986 1 00E 09 1 20E 09 1 40E 09 Bon em

13 Select the appropriate description of the distribution 10 01223345678 11103459 12 035 13 1 Legend 10 0 represents 100 O Uniform O Bell shaped O Skewed Right O Skewed Left Previous Answer d

Question 3 of 15 3 The following data set was collected from a survey 1 8 2 5 2 8 1 3 2 1 2 4 1 8 2 5 3 0 1 3 1 9 2 3 2 1 1 1 1 7 1 5 1 2 2 8 2 4 2 4 1 2 If a cumulative frequency distribution is to be constructed with classes 1 0 1 4 1 5 1 9 2 0 2 4 2 5 2 9 and 3 0 3 4 what is the cumulative frequency of the 2 0 2 4 class 4 Answer Previous Answer 16

Question 14 14 Using the relative frequency distribution below determine the percentage of individuals who are at least 60 inches tall Height inches 50 54 99 55 59 99 60 64 99 65 69 99 Answer Relative Frequency Previous Answer 0 28 0 10 0 18 0 24 0 48 Return to overview

15 What percentage of individuals are 25 27 years of age inclusively 000 T T 22 23 24 25 26 27 Age Round your answer to the nearest hundredths Answer 0 000 Previous Answer 0 21 28 T 29 T 30 4 31

12 What percentage of observations are less than 120 11100223345568 12103458 13 046 14 13 Legend 11 0 represents 110 Round your answer to the nearest hundredths Answer Previous Answer 0 52