Probability Questions and Answers

2 What does one assume when using the relative frequencies of past events to predict future events For example when calculating the probability of a student passing the next assignment in a course question 1 what did you assume about the conditions in the past and the future

Based on advancements in drug therapy a pharmaceutical company is developing Resithan a new treatment for depression A medical researcher for the company is studying the effectiveness of Resithan as compared to their existing drug Exemor A random sample of 573 depressed individuals is selected and treated with Resithan and 293 find relief from their depression A random sample of 408 depressed individuals is independently selected from the first sample and treated with Exemor and 197 find relief from their depression Based on the medical researcher s study can we conclude at the 0 05 level of significance that the proportion p of all depressed individuals taking Resithan who find relief from depression is greater than the proportion all depressed individuals taking Exemor who find relief from depression Perform a one tailed test Then complete the parts below a State the null hypothesis H and the alternative hypothesis H H H 0 b Determine the type of test statistic to use Choose one c Find the value of the test statistic Round to three or more decimal places Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below If necessary consult a list of formulas d Find the p value Round to three or more decimal places e Can we conclude that the proportion of depressed individuals taking Resithan who find relief is greater than the proportion taking Exemor who find relief Yer No 3 x X 5 a X S 2 O O p 0 0 OSO 020 Q olo O O P2 of

An endangered species of birds has a current population of 4200 It is estimated that the population decreases by 4 8 each year a Write an equation to estimate y the number of birds n years from now b Estimate the number of birds 12 years from now ALT 510 PC or ALT FN F10 Mac

Suppose that in Franklin county 69 of households have a dog 45 of households have a dog and a cat You randomly select a household that has a dog What is the probability that it also has a cat Show your work here

Background Morris Saldov conducted a study in Eastern and Central Newfoundland in 1988 to examine public attitudes towards social spending In particular the study tried to determine if knowing someone on public assistance yes no affected one s views on social spending too little about right too much The data from the study is summarized in the table below Too little About right Too much Total Yes No Total 38 6 44 16 13 29 10 9 19 64 28 92 Source Morris Saldov Public Attitudes to Social Spending in Newfoundland Canadian Review of Social Policy 26 November 1990 pages 10 14 Directions Conduct a chi square test for independence to determine if the association between knowing someone on public assistance and views on social spending is statistically significant 1 Choose the correct null and alternative hypotheses Ho There is an association between knowing someone on public assistance and views on social spending Ha There is no association between knowing someone on public assistance and views on social spending Ho There is no association between knowing someone on public assistance and views on social spending Ha There is an association between knowing someone on public assistance and views on social spending 2 Complete the following table of expected counts under the assumption that the null hypothesis is true Round your answers to 1 decimal place Yes Too little About right Too much No 3 Use appropriate technology to compute the value of the test statistic rounded to 2 decimal places and the P value rounded to 3 decimal places P value

What is the storage mode for any given factor vector character O logical O factor numeric

Will tapply throw an error if the INDEX argument is not a factor vector O Yes No

Can factors have ordered levels No O Yes

Are the number of levels of a factor independent of the length of the factor O No Yes

6 The Half life of a radioactive substance is 30 years and you start with 3mg of substance How much is present after 96 years 7 Your car needs repairs and the cost is as follows there is a fixed 250 for parts and 75 per hour for labor a How much will it cost if your car takes 18 hours to repair b Write a linear function that describes the situation Clearly identify all variables used c If you paid 700 to fix the car how many hours of work did they perform on the vehicle

1 point A group of veterinarians at a major veterinary hospital were interested in investigating a possible link between enteroliths stones that form in the colon of horses and diet They decided to conduct a survey of the feeding practices for horses in the hospital s state They created a survey questionnaire and administered it to the owners of every fifth horse being treated at the hospital The sample is a simple random sample Dal a convenience sample a volunteer sample a stratified random sample 0000

1 point The exam scores out of 100 points for all students taking an introductory statistics course are used to construct the following boxplot Exam Score 00 0 100 80 09 40 20 0 If each person increased his or her score by 5 points then the third quartile would increase by 5 points All of the answer options are correct Time Remaining the median score would increase by 5 points the interquartile range would remain unchanged

1 point Suppose that we have two pyramid shaped 4 sided dice with the faces numbered 1 through 4 Suppose that the two dice are rolled and the numbers showing on bottom are added W the probability that this sum is greater than 4 Suggestion Draw a picture of the possible outcome like the one we did in lecture for two ordinary dice

1 point If a hypothesis test is significant at level a 0 05 what is true of the P value P value 0 01 P value 0 05 P value 0 01 P value 0 05

1 point Assume that you are considering buying a car There is a probability of 0 4 that you will purchase a new vehicle and there is a probability of 0 5 that you will purchase a used vehicle There is no probability that you will buy more than one vehicle The probability that you will purchase no vehicle at all is 0 9 0 0000 0 1 1

1 point A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension If the diet is effective the target is to have the average systolic blood pressure of this group be below 150 After six months on the diet an SRS of 28 patients had an average systolic blood pressure of x 143 with standard deviation s 16 The question is whether this if sufficient evidence that the diet is effective in meeting the target Assume the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean u Based on the data the value of the one sample t statistic is 1 76 OO 2 32 1 51 1 94

You randomly select 500 students and observe that 135 of them smoke What is your estimate of the probability that a randomly selected student smokes 1 2 000 0 27 0 17 0 5 because there are two possible outcomes for every student surveyed smoke or don t smoke

AW NA INWA 2 3 4 4 ermine the period 8 12 16 20 24 28 Enter

A large university is divided into six colleges with most students graduating from one of four of these colleges The following bar chart gives the distribution of the percents graduating from these four most popular colleges in 2003 Percent OO 30 25 20 15 10 0 Biobgical sciences il Engineering Math and physical sciences College The percent of students graduating not from either biological sciences is approximately 70 approximately 50 over 80 Business

1 point The regression equation below relates the scores students in an advanced statistics course received for homework completed and for the subsequent midterm exam Homework scores are based on assignments that preceded the exam The maximum homework score a student could obtain was 500 and the maximum midterm score was 350 The regression line that was obtained is given by y 84 4 0 91x If a student had a homework score of 396 the midterm score would be predicted to be rounded to an integer OOO O 282 298 268 276

A marketing consultant is hired by a major restaurant chain that wants to investigate the preferences and spending patterns of lunch customers The CEO of the chain hypothesized that the average customer spends at least 13 50 on lunch A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be x 14 50 Based on previous surveys the restaurant informs the marketing manager that the standard deviation is o 3 50 To address the CEO s conjecture the marketing manager decides to carry out a test of significance The null hypothesis should be Hou 14 50 Hou 13 50 oooo Hou 14 50 H 13 50

In the scatter plot shown below what type of correlation exists between years worked and salary See SCATTER PLOT from the final exam consolidated file O a negative O b neutral c positive d absolute

the wait times in their drive thru for all customers is 3 23 minutes You work for a competitor and you want to test that claim To do so you select a random sample of 40 of the chain s drive thru customers and record the wait time in the drive thru for each Assume it is known that the population standard deviation of the wait times in the drive thru for the hamburger chain s restaurants is 2 91 minutes Based on your sample follow the steps below to construct a 95 confidence interval for the population mean of the wait times in the drive thru for all customers Then state whether the confidence interval you construct contradicts the restaurant chain s claim If necessary consult a list of formulas a Click on Take Sample to see the results from your random sample of 40 customers Take Sample Sample size 0 Point estimate 0 Enter the values of the sample size the point estimate for the population mean the population standard deviation and the critical value you need for your 95 confidence interval Choose the correct critical value from the table of critical values provided When you are done select Compute Population standard deviation 0 Critical value Compute 0 00 Number of customers 0 00 Sample mean Sample standard deviation 2 00 Standard error Margin of error 4 00 95 confidence interval 95 confidence interval b Based on your sample graph the 95 confidence interval for the population mean of the wait times in the drive thru for all customers 5 00 Enter the lower and upper limits on the graph to show your confidence interval For the point enter the restaurant chain s claim of 3 23 minutes 6 00 O No the confidence interval does not contradict the claim The restaurant chain s claim of 3 23 minutes is inside the 95 confidence interval O No the confidence interval does not contradict the claim The restaurant chain s claim of 3 23 minutes is outside the 95 confidence interval Yes the confidence interval contradicts the claim The restaurant chain s claim of 3 23 minutes is inside the 95 confidence interval Population standard deviation 2 91 8 00 Yes the confidence interval contradicts the claim The restaurant chain s claim of 3 23 minutes is outside the 95 confidence interval Critical values x 0 005 2 576 0 010 2 326 0 025 1 960 X 0 050 1 645 0 100 1 282 X c Does the 95 confidence interval you constructed contradict the restaurant chain s claim Choose the best answer from the choices below 5 10 00 10 00

prefer printed textbooks to electronic textbooks You want to test this claim by surveying a random sample of 45 college students Follow the steps below to construct a 90 confidence interval for the population proportion of all college students who prefer printed textbooks to electronic textbooks Then state whether the confidence interval you construct contradicts the study s claim If necessary consult a list of formulas a Click on Take Sample to see the results from the random sample Take Sample Sample size 0 Point estimate 0 Critical value 0 Compute Prefers printed textbooks to electronic textbooks 0 000 Does not prefer printed textbooks to electronic textbooks 0 000 Enter the values of the sample size the point estimate of the population proportion and the critical value you need for your 90 confidence interval Choose the correct critical value from the table of critical values provided When you are done select Compute Standard error Margin of error 90 confidence interval 90 confidence interval 0 500 Number O No the confidence interval does not contradict the claim The proportion 0 45 from the study is inside the 90 confidence interval 27 b Based on your sample graph the 90 confidence interval for the population proportion of all college students who prefer printed textbooks to electronic textbooks O No the confidence interval does not contradict the claim The proportion 0 45 from the study is outside the 90 confidence interval 18 Enter the values for the lower and upper limits on the graph to show your confidence interval For the point enter the claim 0 45 from the study O Yes the confidence interval contradicts the claim The proportion 0 45 from the study is inside the 90 confidence interval O Yes the confidence interval contradicts the claim The proportion 045 from the study is outside the Proportion 0 6 0 4 Critical values 20 005 2 576 20 010 2 326 0 025 1 960 0 050 1 645 20 100 1 282 X X c Does the 90 confidence interval you constructed contradict the claim from the study Choose the best answer from the choices below 1 000 1 000

3 The plot below shows a frequency distribution in gray bars and a normal probability distribution as a red line Frequency Enter here 40 35 30 25 20 15 10 5 0 L 40 44 48 52 56 60 64 68 72 Body mass kg 0 1 0 08 0 06 0 04 0 02 0 Probability How well does the normal probability distribution describe the frequency distribution Which assumptions of the normal probability function seem appropriate for describing the data in the frequency distribution Which do not

Probability Distribution Use the frequency distributions below labeled A D to answer the questions that follow Frequency Frequency 200 A 150 8 8 50 292 888 20 160 140 C 120 100 40 10 20 30 40 50 70 80 90 100 110 120 130 140 Frequency Frequency 180 160 B 140 120 100 80 60 40 20 0 250 200 150 100 50 O 24 D 6 8 10 20 30 40 10 12 50 60 70 80

Please answer the following essay question Consider the data set given below Which of the two options do you think is best for representing the data Explain your reasoning Pay of 10 Individuals at a School 25 30026 62052 000125 00062 052 45 05638 05832 48050 589 23 584 Option 1 Use the mean to describe the pay Option 2 Use the median to describe the pay Answer in paragraph form using complete sentences and include any calculations graphs and labeled diagrams as appropriate

Determine whether the statement is true and justify your response The mean is th measure of central tendency most likely to be affected by outliers

You roll a number cube numbered one to six 12 times P 5 What type of probability is illustrated and why OA experimental the result is based on the number of possible outcomes OB experimental the result is found by repeating an experiment OC theoretical the result is based on the number of possible outcomes O D theoretical the result is found by repeating an experiment

Which of the following best describes a problem that occurs when the plurality method is used 1 point The plurality method only allows comparisons between pairs of candidates and can t be used when there is an uneven number of candidates O The plurality method sums the votes from all choices which takes a long time and can get confusing there are a lot of candidates to choose from O The plurality method only considers the first choice line which leaves out many factors that could affect the outcome of the vote The plurality method only considers the first choice and second choice lines which often vary considerably from subsequent lines

5 Suppose this preference schedule gives the results of an election between three candidates Amy A Beth B and Candice C Based on the plurality method who is the winner of the election number of votes 20 19 5 1st 2nd 3rd CBA BAB ACC O Amy A Beth B Candice C No candidate wins using the plurality method

Solve the following problems involving radicals 10 5 3 3 3

Results from a one way ANOVA indicate that there is not significantly different effect of gender on baseline self compassion F 1 96 effect size np2 125 3 1299 09 P 135 Tukey post hoc analyses indicated that those who identified as Males were type your answer in self compassion than Females p type your answer Males were type your answer Males were type your answer in self compassion than Nonbinary individuals p type your answer self compassion than Transgender individuals p type your answer Females were type your answer in self compassion than Transgender individuals p type your answer See Table 1 for means and standard in self compassion Nonbinary individuals p Nonbinary Females were type your answer in self compassion than Transgender individuals p type your answer type your answer individuals were type your answer deviations Table 1 Means and SDs for Self compassion Among Different Gender Identifications Condition Mean Male Female Nonbinary Transgender 76 82 54 17 72 09 75 64 Standard Deviation 26 29 15 51 30 41 26 58 Submit in

Consider this preference schedule Is there a candidate who could be considered the plurality winner and the majority winner number of votes 14 10 11 1 111 1st 2nd 3rd 4th BCAAC AACD D CDDCA DBBBB Yes candidate B ONo none of the candidates have exactly 50 of all available votes ONo a candidate cannot be both a plurality winner and a majority winner OYes candidate C

1 Suppose you and your friends want to go snowboarding There are four excellent places to go Diamond Bar D Big Boulder B Arrowhead A and Camelback C You ask your friends to rank the locations from their most preferred to their least preferred and compile the responses in a preference table Which location was ranked first by most of your friends 11242 1st ADA BA 2nd D B BAD 3rd BAD CC 4th CCCDB O Arrowhead Big Boulder Camelback Diamond Bar

2 Using the Two Way Frequency Table below answer each question in whole number format or simplest fractional format Male Female Total High School Diploma 16 28 Bachelor s Degree 46 51 Master s Doctoral Degree 3 6 Total 65 a 2pts How many females earned Diploma or Degree b 2pts Probability of a female earning a Bachelor s Degree c 2pts How many males earned a Master Doctoral Degree

1 Using the Two Way Frequency Table below answer each question in decimal format to the nearest 10ths Male Baseball Basketball Football 13 23 15 16 20 31 13 Total Female Total 36 100 a 3pts Choosing a student at random what are the chances of selecting a female student and a basketball player b 3pts Choosing a student at random what are the chances of selecting a male student or a football player c 3pts Choosing a student at random what are the chances of selecting a female student and a football player 33 48 52

In random independent samples of 300 adults and 400 teenagers who watched a certain television show 168 adults and 272 teens indicated that they liked the show Let p be the proportion of all adults watching the show who liked it and let P2 be the proportion of all teens watching the show who liked it Find a 90 confidence interval for P P Then find the lower limit and upper limit of the 90 confidence interval Carry your intermediate computations to at least three decimal places Round your responses to at least three decimal places If necessary consult a list of formulas Lower limit Upper limit 0 X

What does one assume when using the relative frequencies of past events to predict future events For example hen calculating the probability of a student passing the next assignment in a course question 1 what did you ssume about the conditions in the past and the future

3 The linear model that matches this dataset is Tumor Size 1 017 Cigarettes Smoked 0 293 Interpret the slope and y intercept of this linear model in context

Two variables have a positive linear correlation Does the dependent variable increase or decrease as the independent variable increases What if the variables have a negative linear correlation When two variables have a positive linear correlation does the dependent variable increase or decrease as the independent variable increases O Decrease O Increase When two variables have a negative linear correlation does the dependent variable increase or decrease as the independent variable increases O Decrease O Increase

Outpatient Satisfaction Likert Score 0 to 5 Dependent Variable Outpatient Satisfaction Likert Score 0 not satisfied to 5 Very Satisfied vs Time minutes with Doctor in Outpatient Clinic Consultation Scatter Plot n 30 Time minutes with Doctor in Outpatient Clinic Consultation Independent Variable 5 Draw a box and whisker plot for the data set 23 26 25 22 21 22 28 23 29 20 Histogram of Stopping Distance 40 15 60 Stopping Distance 80 100 20 120 4 Sarah is working for a clinic that is trying to find a balance between patient satisfaction and the number of patients their doctors can see in a day The result of her work is the graph at the left a Draw a line of best fit b What is the correlation if any between time spent with a patient and their satisfaction If so what type of correlation is it c Determine the equation of the line curve of best fit if there is one d Based on this data what would the expected satisfaction rate if a doctor spends 12 minutes with a patient 6 Clas Median 7 For the histogram at the left determine the estimated Mean Mode Range Skew 3 What is the relationship between independent and dependent variables the following as discrete D or continuous C data a The number of parts damaged during transportation b The amount of rain that falls during a storm c Weight of truck d Shoe size

43 PCC Lee Name 6 pts Tree diameters in a plot of land are normally distributed with a mean of 14 inches and a standard deviation of 3 2 inches Define draw a label a Normal curve and find the answers using Onlinestatbook You only need to fully label the first drawing a What is the probability that an individual tree has a diameter between 13 inches and 16 3 inches b What is the probability that an individual tree has a diameter less than 12 inches c What is the probability that an individual tree has a diameter of at least 15 inches d Find the cutoff values for the middle 50 of tree diameters including units Show your probability statements and use Onlinestatbook

0 4 0 2 0 1 Answer each of the following questions completely This assignment is worth 15 points 1 6 pts Based on past results found in the Information Please Almanac there is a 0 1919 probability that a baseball World Series will last four games a 0 2121 probability that it will last five games a 0 2223 probability that it will last six games and a 0 3737 probability that it will last seven games a Does the given information describe a probability distribution ExplainX games P Probability 1 These are disjoint outcomes 2 The probabilities sum to 100 4 5 6 0 GRADED PROBLEM SET Module 6 4 5 6 7 0 1919 0 2121 0 2223 0 3737 1 00 0 1919 0 2121 0 2223 7 03737 Assuming that the given information describes a probability distribution find the mean and standard deviation for the number of games in World Series including units 2 3 pts Scores on the Quantitative Reasoning portion of the Graduate Record Exam GRE are Normally distributed with a mean of 153 points and a standard deviation of 7 67 points Define draw and label a Normal curve and use Onlinestatbook to find the cutoff score required to be in the 90th percentile

X 0 1 2 3 P x 0 1 0 15 0 15 0 6 Find the mean of this probability distribution Round your answer to one decimal place Question Help Message instructor Post to forum

Four hundred consumers were surveyed about a new brand of snack food Crunchicles Their age groups and preferences are given in the table Liked Crunchicles Disliked Crunchicles No Preference Total 18 24 25 34 35 55 55 and over Total 130 198 34 82 60 120 224 400 19 14 30 63 22 14 6 42 27 20 24 71 One consumer from the survey is selected at random Use reduced fractions for your responses to each of the following questions What is the probability that the consumer is 18 24 years of age given that he she dislikes Crunchicles What is the probability that the selected consumer dislikes Crunchicles What is the probability that the selected consumer is 35 55 years old or likes Crunchicles If the selected consumer is 70 years old what is the probability that he she likes Crunchicles

Which of the below data sets has the lowest standard deviation You do not need to calculate the exact standard deviations to answer this question 0 1 3 3 3 5 6 0 25 50 100 125 150 1000 0 1 2 3 4 5 6 0 0 0 100 200 200 200

arch center claims that 31 of adults in a certain country would travel into space on a commercial flight if they could afford it In a random sample of 700 adults in that country 34 say that they would travel into space on a commercial flight if they could afford it At a 0 10 is there enough evidence to reject the research center s claim Complete parts a through d below a Identify the claim and state Ho and Ha Identify the claim in this scenario Select the correct choice below and fill in the answer box to complete your choice Type an integer or a decimal Do not round A The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not OB At least OC No more than it O D of adults in the country would travel into space on a commercial flight if they could afford it Let p be the population proportion of successes where a success is an adult in the country who would travel into space on a commercial flight if they could afford it State Ho and H Select the correct choice below and fill in the answer boxes to complete your choice Round to two decimal places as needed OA Ho p H ps of adults in the country would travel into space on a commercial flight if they could afford it of adults in the country would travel into space on a commercial flight if they could afford OD Ho P Ha p OB Ho P OE Ho p2 Ha p b Use technology to find the P value Identify the standardized test statistic 2 0 Round to two decimal places as needed Identify the P value P Round to three decimal places as needed Ha p the null hypothesis There OC Ho Ps H p c Decide whether to reject or fail to reject the null hypothesis and d interpret the decision in the context of the original claim enough evidence to OF Ho P Ha p the research center s claim

The distribution of blood types for 100 Americans is listed in the table If one donor is selected at random find the probability of selecting a person with blood type A Blood Type O Number 37 OA 0 68 OB 0 4 OC 0 34 OD 0 45 O A 6 34 A B 6 10 B 2 AB AB 4 1

The distribution of Master s degrees conferred by a university is listed in the table Major Frequency Mathematics English Engineering Business Education 216 207 72 176 222 What is the probability that a randomly selected student graduating with a Master s degree has a major of Engineering Round your answer to three decimal places OA 0 081 B 0 014 OC 0 919 O D 0 986