Probability Questions and Answers

3 A bag of marbles contains 10 Red and 5 Blue Marbles Find the probability a Red is selected first followed by a Blue if selection is done a With replacement b Without replacement

Use the data in the following table which lists drive thru order accuracy at popular fast food chains Assume that orders are randomly selected from those included in the table Order Accurate Order Not Accurate Drive thru Restaurant C 249 32 A 324 35 B 263 57 D 121 18 If two orders are selected find the probability that they are both from Restaurant D a Assume that the selections are made with replacement Are the events independent b Assume that the selections are made without replacement Are the events independent a Assume that the selections are made with replacement Are the events independent The probability of getting two orders from Restaurant D is The events the first order the probability of the choice of the second order Do not round until the final answer Round to four decimal places as needed independent because choosing

This question 1 point s possible You are given the sample mean and the population standard deviation Use this information to construct the 90 and 95 confidence intervals for the population mean Interpret the results and compare the widths of the confidence intervals From a random sample of 46 business days the mean closing price of a certain stock was 108 56 Assume the population standard deviation is 11 41 The 90 confidence interval is Round to two decimal places as needed The 95 confidence interval is Round to two decimal places as needed Which interval is wider Choose the correct answer below The 90 confidence interval The 95 confidence interval Interpret the results Submit test OA You can be certain that the population mean price of the stock is either between the lower bounds of the 90 and 95 confidence intervals or the upper bounds of the 90 and 95 confidence intervals O B You can be 90 confident that the population mean price of the stock is outside the bounds of the 90 confidence interval and 95 confident for the 95 interval C You can be certain that the closing price of the stock was within the 90 confidence interval for approximately 41 of the 46 days and was within the 95 confidence interval for approximately 44 of the 46 days D You can be 90 confident that the population mean price of the stock is between the bounds of the 90 confidence interval and 95 confident for the 95 interval

Each year a nationally recognized publication conducts its Survey of America s Best Graduate and Professional Schools An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable A simple linear regression of SALARY versus GMAT using 25 data points shown below bo 92040 b 228 R 0 66 Give a practical interpretation of R 0 66 OA We estimate SALARY to increase 66 for every 1 point increase in GMAT We can predict SALARY correctly 66 of the time using GMAT in a straight line model OC 66 of the differences in SALARY are caused by differences in GMAT scores O B r 0 81 D 66 of the sample variation in SALARY can be explained by using GMAT in a straight line model

The following boxplot represents the IQ scores of 30 randomly selected students Identify a possible 5 number summary for these IQ scores in this boxplot 95 100 105 110 115 IQ SCORES OA 92 98 106 110 119 OB 95 100 105 110 115 OC 87 96 103 108 116 OD 90 95 100 105 110

A simple random sample of 100 batteries is selected from a process that produces batteries with a mean lifetime of 32 hours and a standard deviation of 3 hours Thus the standard deviation of the sampling distribution is equal to 0 3 If the sample size is changed to 400 what is the new standard deviation of the sampling distribution OA 0 01 OB 0 60 OC 0 30 OD 0 15 Here is the link to the formula sheet that you are allowed to use on this exam Math

Male Player Female Player TOTAL A 0 3897 OB 0 4375 C 0 6103 Challenge Challenge TOTAL Accepted Rejected D 0 0012 201 126 327 288 224 512 489 Results of Player Challenges in the U S Open Tennis Tournament are displayed in the table by gender and by result If one of the challenges is randomly selected find the probability of getting a challenge that was rejected Results are rounded to 4 decimals 350 839

A random sample of 30 digital cameras is selected and divided into two groups One group uses a brand name battery while the other uses a generic plain label battery All variables beside battery type are controlled Pictures are taken under identical conditions and the battery life of the two groups is compared This is an example of an OA observational study B designed experiment ere is the link to the formula sheet that you are allowed to use on this exam Math 01 FormulaSheet

1 An automobile dealer gathered data concerning the age and the type of vehicle that was purchased from a random sample of the people that bought vehicles from them in the past year The data is contained in the table below Age of Buyer 59 years 60 years and older Total 15 50 20 40 17 64 52 154 Type of Vehicle Purchased Truck Car SUV Total 0 1104 0 6429 0 3269 0 2656 0 39 years 40 O 20 25 10 12 47 10 10 35 55 Suppose a buyer is selected at random from this group what is the probability that the buyer is in the age group 40 59 and purchased an SUV W

The monthly utility bills in a city are normally distributed with a mean of 100 and a standard deviation of 13 Find the probability that a randomly selected utility bill is a less than 68 b between 83 and 90 and c more than 110 a The probability that a randomly selected utility bill is less than 68 is Round to four decimal places as needed b The probability that a randomly selected utility bill is between 83 and 90 is Round to four decimal places as needed c The probability that a randomly selected utility bill is more than 110 is four decimal places as needed

In a survey of a group of men the heights in the 20 29 age group were normally distributed with a mean of 69 3 inches and a standard deviation of 3 0 inches A study participant is randomly selected Complete parts a through d below a Find the probability that a study participant has a height that is less than 67 inches The probability that the study participant selected at random is less than 67 inches tall is Round to four decimal places as needed b Find the probability that a study participant has a height that is between 67 and 71 inches The probability that the study participant selected at random is between 67 and 71 inches tall is Round to four decimal places as needed c Find the probability that a study participant has a height that is more than 71 inches The probability that the study participant selected at random is more than 71 inches tall is d Identify any unusual events Explain your reasoning Choose the correct answer below Round to four decimal places as needed A The events in parts a and c are unusual because its probabilities are less than 0 05 OB The event in part a is unusual because its probability is less than 0 05 OC The events in parts a b and c are unusual because all of their probabilities are less than 0 05 D There are no unusual events because all the probabilities are greater than 0 05

he table below displays results from experiments with polygraph instruments Find the positive predictive value for the test That is find the probability that the subject lied given that the test yields a pos Did the Subject Actually Lie No Did Not Lie Yes Lied 40 8 Positive test results Negative test results The probability is 10 32

The number of students using the School Bus per day is found in the distribution below X P X 15 0 3 Standard 25 0 4 Variance Select 313 29 None of these answers 111 65 10 0 2 12 Find the mean variance and the standard deviation for this probability distribution Mean Select 0 1

Determine if the system is commutative 1 B H Y B B Y Y O Yes O No H Y H B Is the system commutative Y H B H

the circle Part A Write the equation of the circle Part B Prove point B 4 9 is on the circle Part C The general form of the equation of circle A is x y 14 10y 49 0 Liam was asked to confirm by completing the square that this is the equation of circle A His work is below x y 14x 10y 49 0 1 move the constant x y 14x 10y 49 x 14x 49 y 10g 25 49 2 re arrange and complete the square x 7 y 5 49 3 write in factored form

3 Suppose that the number of ounces x of ground coffee that is packaged into cans by a dispenser is normally distributed with a mean of 48 and a standard deviation of 0 3 a What is the probability that x is between 47 7 and 48 45 b What is the probability that x is at most 48 78 c What is the probability that x exceeds 47 04 d What value of x is exceeded by only 10 of all such cans

If the area to the left of z in a normal distribution is 0 2 what is the area to the right of x Answer If the area to the right of z in a normal distribution is 0 2 what is the area to the left of Answer

A commonly cited standard for one way length duration of school bus rides for elementary school children is 30 minutes A local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one way commute time If they determine that the average commute time of students in their district is significantly higher than the commonly cited standard they will invest in increasing the number of school buses to help shorten commute time What would a Type 2 error mean in this context The local government decides that the average commute time is 30 minutes The local government decides that the data provide convincing evidence of an average commute time higher than 30 minutes when the true average commute time is in fact 30 minutes O The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes when the true average commute time is in fact higher than 30 minutes The local government decides that the data do not provide convincing evidence of an average commute time different than 30 minutes when the true average commute time is in fact 30 minutes

A 2011 survey by the Bureau of Labor Statistics reported that 91 of Americans have paid leave In January 2012 a random survey of 1000 workers showed that 89 had paid leave The resulting p value is 0 0271 thus the null hypothesis is rejected It is concluded that there has been a decrease in the proportion of people who have paid leave from 2011 to January 2012 What type of error is possible in this situation type I type II neither both

ions Exan tion of the number of televisions in the homes of 90 community college students a According to the histogram about how many homes do not have a television b How many televisions are in the homes that have the most televisions c How many homes have three televisions d How many homes have six or more televisions e What proportion of homes have six or more televisions Frequency 30 25 20 15 10 5 0 0 2 4 6 Number of TVs 8

magazine com 2011 11 what we know about wealth a In truth the top fifth in terms of wealth actually held about what per centage of the wealth b Which figures Ideal Estimate or Truth show the least variation c Which figures Ideal Estimate or Truth show the most variation d Do people making estimates tend to underestimate or to overestimate the proportion of wealth held by the top 20 Percentage 90 80 Percentage 70 50 40 30 20 10 0 7 10 5 30 25 20 15 L 0 Top Fifth O Education The graph shows the education of residents of and Acres and Oxnard both of which are towns in Ventura mty in California c Some people believe that women tend to lean more than men toward liberal political positions such as those advocated by the Democrats Compare the graphs for Exercises 2 41 and 2 42 Do you see evidence of this Explain hh 2nd Middle 4th Fifth Wealth in Fifths in US 1000 Ideal Estimate Truth Bottom Fifth Fifth Fifth Strong Dem Dem not strong Bar Chart of Political Party for Women Other 10 Rep not strong Strong Rep 0 Strong Dem Dem not strong Pie Chart of Political Party for Men Percentage SECTION EXERCISES 50 2 42 Political Party Affiliation Women The 2012 General Social Survey GSS asked its respondents to report their political party affiliation The graphs show the results for 1081 women a Which political affiliation has the most women b What political affiliation has the second largest number of women Is this easier to determine with the bar chart or with the pie chart Expla 40 Other 30 20 Rep not strong 2 44 Retail Car Sales With gas prices rising as they between 1985 and 2007 you might expect people to mo buying smaller cars Compare the types of cars sold in 1 and 2007 as shown in the figure Source 2009 World A Book of Facts a Which type of car sold the most in all three years b What is the trend for small cars Has a higher or a lower small cars sold in more recent years c What is the trend for large cars 10 0 Strong Rep Party Strong Dem Dem not strong Other 1985 Rep not strong Strong Rep Car Sales CHAPTER 2 2000 2007

2 6 Exercise Hours The histogram shows the distribution of self reported numbers of hours of exercise per week for 50 commu nity college students This graph uses a right hand rule Someone who exercised for exactly 4 hours would be in the third bin the bin to the right of 4 Frequency 18 16 14 12 IT 08642O 10 7 048 12 16 20 Exercise Hours per week a According to the histogram there are two possible values for the max mum number of hours of exercise What are they b How many people exercised 0 or 1 hour less than 2 hours 1 10

2 2 Cholesterol Levels The dotplot shows the cholesterol level of 93 adults from the 2010 NHANES data 0 000 50 100 150 200 250 300 350 400 450 500 550 Cholesterol mg dL a A total cholesterol level of 240 mg dL milligrams per deciliter or more is considered unhealthy Report the number of people in this group with unhealthy cholesterol levels b Knowing there are a total of 93 people in this sample report the per centage of people with unhealthy total cholesterol levels How does this compare with an estimate from 2010 that 18 of people in the

Data from the Bureau of Labor Statistics indicates that in a certain month 37 3 of the labor force had a high school diploma or fewer years of education 26 6 ha some college or an associate s degree and 36 1 had a bachelor s degree or more education Of those with a high school diploma or fewer years of education 6 7 were unemployed Of those with some college or an associate s degree 6 4 were unemployed and of those with a bachelor s degree or more education 4 8 we unemployed Find the probability that a randomly chosen labor force participant has a bachelor s degree or more education given that he or she is employed The probability is Type an integer or decimal rounded to three decimal places as needed CHE

6 10 points John and Jim are two brothers and they are going to the same school According to the past experience on each morning the probability that John is late to school is 25 the probability that Jim is late to school is 18 and the probability that they are both late is 10 a In a given morning what is the probability that at least one of the brothers is late to school b In a given moming what is the probability that Jim is present on time

1 000 Simulate this model for 50 trials and a production quantity of 140 What is the average profit proposal and determine a distribution of profits using the provided discrete distributions for the unit cost demand and fixed costs Price is fixed at Click here to view the discrete distributions Click here to view a sample of 50 simulation trial results Set up a lookup table for the unit cost Type integers or decimals Do not round Use ascending order Unit Cost Probability Lower Limit Upper Limit 400 0 25 600 0 35 700 0 20 800 0 20 400 600 700 800 Discrete Distributions Unit Cost Probability 400 0 25 600 700 800 Demand 120 140 160 0 35 0 20 0 20 45 000 50 000 55 000 Probability 0 25 0 55 0 20 Fixed Costs Probability 0 25 0 50 0 25 X Simulation Results 42 000 29 000 1 000 42 000 9 000 14 000 42 000 39 000 17 000 19 000 47 000 9 000 19 000 19 000 29 000 3 000 27 000 19 000 3 000 19 000 Print 11 000 9 000 6 000 22 000 29 000 22 000 22 000 13 000 34 000 3 000 8 000 19 000 28 000 19 000 29 000 22 000 22 000 11 000 8 000 22 000 Done 11 000 6 000 13 000 22 000 19 000 27 000 17 000 17 000 13 000 6 000

A student was asked to find a 99 confidence interval for the proportion of students who take notes using data from a random sample of size n 81 Which of the following is a correct interpretation of the interval 0 1 p 0 29 Check all that are correct There is a 99 chance that the proportion of notetakers in a sample of 81 students will be between 0 1 and 0 29 The proportion of all students who take notes is between 0 1 and 0 29 99 of the time With 99 confidence a randomly selected student takes notes in a proportion of their classes that is between 0 1 and 0 29 There is a 99 chance that the proportion of the population is between 0 1 and 0 29 With 99 confidence the proportion of all students who take notes is between 0 1 and 0 38

A student was asked to find a 90 confidence interval for the proportion of Students who take notes using data from a random sample of size n 75 Which of the following is a correct interpretation of the confidence interval 0 1 p 0 21 Check all that are correct O There is a 90 chance that the proportion of notetakers in a sample of 75 students will be between 0 1 and 0 21 O With 90 confidence a randomly selected student takes notes in a proportion of their classes that is between 0 1 and 0 21 O With 90 confidence the proportion of All students who take notes is between 0 1 and 0 21

A student was asked to find a 90 confidence interval for widget width using data from a random sample of size n 27 Which of the following is a correct interpretation of the interval 13 p 30 47 Check all that are correct With 90 confidence the mean width of all widgets is between 13 and 30 4 With 90 confidence the mean width of a randomly selected widget will be between 13 and 30 4 The mean width of all widgets is between 13 and 30 4 90 of the time We know this is true because the mean of our sample is between 13 and 30 4 There is a 90 chance that the mean of the population is between 13 and 30 4 There is a 90 chance that the mean of a sample of 27 widgets will be between 13 and 30 4

14 Following is an incomplete table showing the results of a survey of students some of whom wore good luck amulets while taking their recent math exam the table A is the event that the participant wore an amulet and F is the event that the participant failed the test F F A 25 If it is found that the amulet has no effect on performance in the test what is the missing value A 125 1375

probability in each case a Two coins are tossed E The first coin comes up heads F The result is no heads P E F Check Clear Give the exact answer not a decimal approximation b A die is thrown E The result is an odd number F The result is at most 4 P E F Check Clear Give the exact answer not a decimal approximation c A pair of distinguishable dice are thrown and the numbers facing up are observed E The sum is less than 3 F The first die cc Check Clear P E F

Its of a new acne medication Condition improved 1 No change N Condition worse W c P LON Total Check Clear Used medication M Used placebo L 400 500 400 500 200 500 1500 Let M be the event that a participant used the medication L the event that a participant used the placebo I the event a the participant s condition improved a so on as shown by the letters in the headings Find the relative frequency in each case a P I b E It is not the case that a participant used the medication P E Check Clear Check Clear 1000 d F A participant used the medication or saw their condition improve P F Check Clear Total 900 900 700 2500 GA participant who used the placebo saw no change in their condition

in each case You may be given more information than you need a P E F 8 P FE 364 P En F 2 P F Check Clear Accurate to 2 decimal places b P E 5 P F 4 P EnF 24 P EF Check Clear Accurate to 2 decimal places c P E F 08 P E 1 P F 75 P EUF Check Clear Accurate to 2 decimal places d P E 0 7 P F 0 25 E F are independent P FE Check Clear

monog he Moon is in the Seventh House or both 81 of the time a What percentage of time is the moon is in the Seventh House at the same time that Jupiter aligns with Mars Answer Check Clear b What percentage of time is Jupiter does not align with Mars Answer Check Clear c What percentage of time is either Jupiter does not align with Mars or the Moon is not in the Seventh House or neither Clear

Determine whether the events E and F are independent in each case a P E 95 P F 50 P En F 480 b P E 35 P F 46 P EUF 649 c P E 900 P F 200 P E F 900 O Independent O Dependent Independent O Dependent O Independent O Dependent

wo dice one red one green are cast and the uppermost numbers are observed Test the given events for independence in each case E The red die comes up 3 F The green die comes up even a c d e E The red die comes up 1 F The sum is even E The red die comes up 6 F The sum is 8 O Independent O Dependent Independent Dependent O Independent O Dependent E The sum is 3 F The green die comes up even E Neither die is 2 F Both die show the same number O Independent O Dependent Independent O Dependent

13 Here is a table showing fictitious trial results of a new acne medication a P IM Condition improved 1 No change N Condition worse W Check Clear Give the exact answer not a decimal approximation Check Clear b P MI Total c P I Assume that a participant is selected at random Let M be the event that the participant used the medication L the event that the participant used the placebo I the event that the participant s condition improved and so on as shown by the letters in the headings Give the exact answer not a decimal approximation Check Clear Give the exact answer not a decimal approximation Check Clear d P M Give the exact answer not a decimal approximation Used medication M Used placebo L 50 100 90 710 900 e Test the events I and L for independence Independent O Dependent 10 40 100 Independent Total 150 100 750 1000

3 Here is a table showing the auction prices of a collection of very rare paint by number reproductions of Jackson Pollock paintings Price 0 999 1 000 1999 2 000 2 999 3 000 3 999 4 000 4 999 5 000 2 Number sold 1 6 8 1 0 Calculate the relative frequency of the given event E in each case a A painting is auctioned for between 2 000 and 4 999 P E Check Clear b A painting is auctioned for at least 4 000 P E Check Clear c A painting is not auctioned for between 1 000 and 4 999

Calculate the modeled probability in each case Assume coins and dice are distinguishable and fair All answers should be exact use fractions rather than ecimal approximations a n S 180 n E P E 60 Assume that the outcomes are equally likely Check Clear b 3 coins are tossed E The result is no heads P E Check Clear c A die is thrown E The result is an even number P E Check Clear d A pair of distinguishable dice are thrown and the sum of the numbers facing up is noted E The result is equal to 13

1 In each of the following find the cardinali a 4 coins are tossed E The resul n S Check n E Check

age C MATH1507 M N O P Q R S Mathematics Il for the Biol Health coverage frequencies The Behaviora hone survey designed to identify risk factors in t following table summarizes two variables for the ribes whether each respondent had health insura

Consider the following 2 way table Note that the units of observation is cats and that the rows are evels of the factor meows and that the columns are levels of the factor owner income The total number of observational units is 390 frequent medium infrequent Within this collection the proportion of medium meows is closest to D0 25641 00 29487 D014103 D0 17949 00 2 00 07692 D0 14103 0 17949 Within this collection the proportion of low owner income is closest to 00 42308 0 07692 D0 7 0 25641 high 100 70 55 low 30 45 90 0 17949 0 14103 0 11538 Within this collection the proportion of cats that are both medium meows and low owner income is closest to 107

The correlation coefficient wonld increase We know that b r s y s x The added point will increase s x more than it will increase s y so s y s r will be less than 1 If the slope is to stay the same r must increase

14 Suppose that your six exam grades in a course are 84 73 62 85 93 and 85 Compute your final course grade 90 100 A 80 89 B 70 79 C 60 69 D below 60 F using the a Mean b median

On an American roulette wheel there are 18 red numbers 18 black numbers plus two green numbers 0 and 00 If you bet SN on red you win SN if a red number comes up i e you get 2N back your original bet plus your SN profit if a black or green number comes up you lose your N bet Find the expected payoff of a 5 bet on red

The red blood cell counts in millions of cells per microliter for a population of adult males can be approximated by a normal distribution with a mean of 5 1 million cells per microliter and a standar deviation of 0 4 million cells per microliter a What is the minimum red blood cell count that can be in the top 29 of counts b What is the maximum red blood cell count that can be in the bottom 15 of counts a The minimum red blood cell count is Round to two decimal places as needed b The maximum red blood cell count is Round to two decimal places as needed million cells per microliter million cells per microliter COLLE

The weights of bags of baby carrots are normally distributed with a mean of 33 ounces and a standard deviation of 0 32 ounce Bags in the upper 4 5 are too heavy and must be repackaged What is the most a bag of baby carrots can weigh and not need to be repackaged Click here to view Page 1 of the Standard Normal Table Click here to view Page 2 of the Standard Normal Table A bag of baby carrots can weigh at most Round to two decimal places as needed ounces without needing to be repackaged CD

Provide an appropriate response Use the Standard Normal Table to find the probability An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with 15 5 and o 3 6 What is the probabil that during a given week the airline will lose less than 20 suitcases OA 0 3944 B 0 8944 OC 0 4040 OD 0 1056 CO

Ivanna has scored 81 82 73 92 and 95 on her previous five tests What score does she need on her next test so that her average mean is 81 0 X

The birth weights to the nearest pound of a sample of 36 newborn babies at a certain hospital are given in the following table along with the number of babies at each birth weight Number of babies Birth weight in pounds B 2 P pounds 7 16 11 5 6 7 Find the mean birth weight of these 36 babies Round your answer to at least one decimal place 8 X S