# Statistics Questions

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Statistics

Probability1 Suppose that a family has 7 children Also suppose that the probability of having a boy based on the gender assigned at birth is Find the probability that the family has no more than 5 2 The probability that the family has no more than 5 boys is Type an integer or a simplified fraction

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ProbabilityA die is rolled 9 times Find the probability of rolling exactly 1 The probability is Round to four decimal places as needed

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ProbabilityOne option in a roulette game is to bet 8 on red There are 18 red compartments 18 black compartments and two compartments that are neither red nor black If the ball lands on red you ge keep the 8 you paid to play the game and you are awarded 8 If the ball lands elsewhere you are awarded nothing and the 8 that you bet is collected Find the expected payback for this roul game if you bet 8 on red The expected payback is Round to the nearest cent as needed

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Probability1 Suppose that a family has 4 children Also suppose that the probability of having a girl based on the gender assigned at birth is Find the probability that the family has the follo 2 Exactly 2 girls and 2 boys The probability is Type an integer or a simplified fraction GCEER

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StatisticsA container contains 6 diesel engines The company chooses 4 engines at random and will not ship the container if any of the engines chosen are defective Find the probability th be shipped even though it contains 2 defective engines The probability the container will be shipped is Round to the nearest thousandth as needed

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Statisticssurvey finds that customers are overcharged by price scanning systems on average on 1 70 of items Suppose a customer purchases 10 items Find th A customer is not overcharged for any item The probability is Round to four decimal places as needed

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StatisticsA raffle offers a first prize of 500 and 3 second prizes of 80 each One ticket costs 1 and 600 tickets are sold Find the expected payback for a person who buys 1 ticket Is this a fair The expected payback for a person who buys 1 ticket is Round to two decimal places as needed CELOR

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Probabilityhipment of 9 printers contains 3 that are defective Find the probability that a sample of size 3 drawn from the 9 will not contain a defective probability is pe an integer or a simplified fraction COLLE

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StatisticsData for motor vehicle production in a country for the years 1997 to 2004 are given in the table Year 1997 1998 1999 2000 2001 2002 2003 2004 Thousands 1 537 1 628 1 800 2 009 2 391 3 251 4 415 5 071 A Find the least squares line for the data using x 0 for 1990 y 0 Use integers or decimals for any numbers in the expression Do not round until the final answer Then round to nearest tenth as needed

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ProbabilityHere is a bivariate data set x 1 7 67 5 46 5 12 6 23 9 r y 65 4 173 8 107 4 88 4 80 1 4 7 87 9 4 35 2 4 7 8 9 37 1 42 3 47 3 105 9 35 4 133 6 16 9 9 8 122 8 83 7 7 3 39 2 73 1 56 2 9 2 25 3 15 4 29 4 26 3 8 6 18 3 This data can be downloaded as a csv file with this link Download CSV 64 1 40 8 Find the correlation coefficient and report it accurate to three decimal places What proportion of the variation in y can be explained by the variation in the values of x Report answer as a percentage accurate to one decimal place m

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StatisticsThe following table lists the birth weights in pounds x and the lengths in inches y for a set of newborn babies at a local hospital Birth Weight in Pounds Length in Inches y 9 Birth Weights and Lengths 8 4 11 5 18 17 16 21 17 3 16 6 16 3 6 3 16 16 16 Copy Data tep 1 of 2 Find an equation of the least squares regression line Round your answer to three decimal places if necessary

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StatisticsA certain municipality recycled seven times as many tons of yard waste as aluminum in one year If the total amount recycled was 1584 tons how much yard waste and how much aluminus was recycled tons of yard waste were recycled math Tute an CELER

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StatisticsThe following table gives the monthly premiums for an insurance policy on people of various ages a Find an exponential function that models the monthly premium as a function of age b Find the quadratic function that is the best fit for the data c Graph each function with the data points to determine which model is the better fit GELER Age 35 40 45 50 55 Monthly Premium 122 173 262 397 630 Age 60 65 70 75 Full data set Monthly Premium S 989 1531 2878 5550 a The exponential function that models the data is y Use Integers or decimals rounded to the nearest thousandth as needed for any numbers in the expression

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ProbabilityHere is a bivariate data set X 51 70 8 57 6 19 2 y 21 25 3 155 8 139 6 62 4 64 3 67 2 114 4 58 2 64 8 This data can be downloaded as a csv file with this link Download CSV Find the correlation coefficient and report it accurate to three decimal places r What proportion of the variation in y can be explained by the variation in the values of x Report answer as a percentage accurate to one decimal place R

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Statistics12 points A toy manufacturer asks a developmental psychologist to test children s response to a new product Specifically the manufacturer wants to know how long on average the toy captures children s attention The psychologist tests a sample of 49 children and measures how long they play with the toy before they get bored and want something else to play with This sample had a mean time of 18 minutes and a standard deviation of 3 minutes Construct a 99 confidence interval estimate for the mean number of minutes all children play with the toy before they get bored

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StatisticsThe correlation between a student s homework grade homework x and their average exam score y is T 0 45 What is the coefficient of determination Round your answer to three decimal places The coofficient of determination tells us that approximately of the variation in

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StatisticsA Kaiser Permanente pamphlet on prostate cancer screening states that out of every 100 men screened we would typically expect 10 to have a positive PSA test result 3 who actually have prostate cancer and the other 7 not actually having prostate cancer and 90 to have a negative PST test result 1 who actually has prostate cancer and the other 89 do not 1 Use this information to obtain the sensitivity of the PSA screening test P positive test result prostate cancer Your result is a value Select 2 Obtain the positive predictive value of the PSA screening test in this population P prostate cancer positive test result Your result is a value Select

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StatisticsAt a given temperature you measure the speed of each molecule in a gas sample Which of the following statements is TRUE about that sample If you drew a histogram of the speeds and considered the average and 2 average there will be more counts in the bar containing the average O All molecules will have the same speed If the temperature increased the average speed would also increase

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StatisticsThe CDC reports that there were 3 855 500 births in the United States for the year 2017 The report breaks down the births by age of the mother and by type of delivery vaginal cesarean or unknown not stated as shown below Mother s age Under 20 20 24 25 29 30 34 35 39 40 54 All ages Type of delivery Vaginal 156 727 566 567 784 533 717 581 331 394 64 208 2 621 010 Cesarean Not Stated 39 459 108 197 719 494 338 366 678 373 825 511 223 119 283 59 851 77 1 232 339 2 151 All delivery types 196 294 764 780 1 123 577 1 091 917 554 796 124 136 3 855 500 Examine carefully the information provided and obtain the following probabilities for the sample space of U S births in 2017 1 P 20 24 cesarean Select 2 P cesarean and 20 24 Select 3 P cesarean 20 24 Select 4 In 2017 in the United States Select 24 were delivered via cesarean of births to young mothers ages 20

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StatisticsQuestion 1 Select the TRUE statements below You have a mixed gas sample at 2 atm the pressure of each species is also 2 0atm Total pressure of a system is equal to the sum of the partial pressures The partial pressure is proportional to the mole fraction 1 pts

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StatisticsThe UC Undergraduate Experience Survey is a census survey administered to all undergraduates enrolled at University of California campuses For the first time in spring 2016 the survey included questions about food insecurity defined as an inadequate food intake for financial reasons at some point in the past 12 months and homelessness defined as not having reliable housing at some point in the past 12 months We can use the findings to create a probability model describing the population of UC undergraduate students in 2016 Students who experienced homelessness were more likely to experience food insecurity Among students who reported having experienced homelessness 77 percent also reported having experienced food insecurity compared to 42 percent who reported not having experienced homelessness Figure 7 About nine percent of undergraduate students who reported experiencing food insecurity also reported having been homeless four percentage points higher than the undergraduate prevalence overall 44 Overall Food Insecurity 42 Not Homeless 77 Homeless 5 Overall Homelessness 2 Food Secure 9 Food Insecure Figure 7 Comparisons of undergraduates experiencing food insecurity and homelessness Let s use the following notation for the sample space of UC undergraduate students in 2016 H homeless not H not homeless FI food insecure not FI food secure not insecure You may want to start by labeling each value cited using probability notation to make sure that you understand what they actually represent 1 The value 77 represents the probability Select 2 In 2016 what was the probability that a randomly selected UC undergrad had experienced both food insecurity and homelessness at some point in the past 12 months Your answer falls within the range Select 3 Food insecurity and homelessness are Select undergrad population The UCI Basic Needs Center offers a variety of services to UCI students to help them meet their basic needs food pantry CalFresh application assistance emergency food and on campus housing outcomes in the UC

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StatisticsTrue false The sensitivity and the positive predictive value of a test will typically have fairly similar values O True O False

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ProbabilityWhich notation represents the conditional probability of the event A given event B O P A or B O P BIA O P AB O P A and B

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ProbabilityIn probability which of the following visual displays shows conditional probability values None of these displays do Venn diagram two way table O probability tree

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ProbabilityThe notation for conditional probabilities always follows which general format O Pla specific outcome and some relevant information O Pla specific outcome some relevant information O P some relevant information a specific outcome O either P a specific outcome some relevant information or P some relevant information a specific outcome whichever format you like best

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StatisticsIn the pool example we concluded that events DF and IC are dependent events because O IC causes pool filters to get dirty faster O a pool can have both IC and DF O we found that P IC DF was different from P IC O a pool can have DF and not have IC

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ProbabilityIf 6ft stands for a human height of at least 6 feet then P 6ft man is the probability O of being a man but not one who is 6ft tall O of being 6ft tall if the person is a man O of being a man and being 6ft tall O of being 6ft tall but not a man of being a man if the person is 6ft tall O of being neither a man nor 6ft tall

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ProbabilityThe probability of the entire sample space O can be any strictly positive value O is always equal to 1 O is usually a value smaller than 1 but always greater than 0 O can be any positive value

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ProbabilityQuestion 1 Which of the following was offered as an example of discrete sample space O zip codes O blood types O cholesterol levels amazon ratings

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StatisticsIn probability which represents the intersection of the event A and the event B OP A or B OP A and B O P sample space O P AB O P BIA

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Statisticsrandom sample from the population and perform a hypothesis test at the 0 10 level of significance To start this test you write the null hypothesis Ho and the alternative hypothesis H as follows Ho 7 H 7 Suppose you also know the following information The critical values are 1 645 and 1 645 rounded to 3 decimal places The value of the test statistic is 0 688 rounded to 3 decimal places a Complete the steps below to show the rejection region s and the value of the test statistic for this test Standard Normal Distribution Step 1 Select one tailed or two tailed O One tailed O Two tailed Step 2 Enter the critical value s Round to 3 decimal places Step 3 Enter the test statistic Round to 3 decimal places The null hypothesis should be rejected The null hypothesis should not be rejected 04 X 03 S 02 b Based on your answer to part a choose the correct statement O The value of the test statistic lies in the rejection region O The value of the test statistic doesn t lie in the rejection region 0 3 c Based on your answer to part b which statement below is true at the 0 10 level of significance X

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StatisticsPieta uses Cormack Jolly Seber models to estimate annual apparent survival of Laysan Albatross based on resighting data collected at Midway Atoll where they nest Based on these data she estimates annual apparent survival of 0 950 SE 0 005 She also has band recovery data available for birds that were found dead throughout the entire Pacific Ocean and based on these data she estimates that annual survival S is 0 950 SE 0 005 Considering these two estimates in aggregate what is your best numerical estimate of permanent emigration of breeding Laysan Albatross from Midway Atoll

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StatisticsA car leasing firm s records indicate that the mean number of miles driven annually in its cars has been about 17 500 miles The firm suspects that this number has decreased this past year Suppose that the firm wishes to choose a small sample of driving distances from the past year and carry out a hypothesis test for its suspicion State the null hypothesis and the alternative hypothesis that it would use for this test Ho H 0 3 4 XI O P S

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StatisticsDuring a 6 year study Daunte documents annual moose survival by monitoring a samp of radiomarked individuals He obtains the following 6 estimates of annual survival and calculates their mean and standard deviation sd Which statement best describes the estimate sd S 0 0453 S c 0 883 0 787 0 914 0 825 0 838 0 870 mean S 1 0 8528333 sd S 1 0 04533174 This is a measure of process variation or truc variation in annual survival This is a measure of noise or measurement error in annual survival This is a measure of both process variation and noise

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StatisticsAnnual survival of adult Northern Pintails is approximately 0 7 Given this value what is their average future lifespan in years

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Statisticshe manager at a local fast food restaurant is doing an inventory of the breakfast items sold last week to determine the least and most popular items serv listed in the following table Item Served Chicken Biscuit Sausage Biscuit Ham Biscuit Bacon Egg Biscuit Gravy Biscuit Oatmeal and Fruit Breakfast Burrito Monday Tuesday 11 14 23 15 38 38 30 17 18 10 37 10 10 29 Copy Data Step 1 of 2 Determine the frequency of the least popular item sold last week Wednesday 24 25 26 29 17 32 16 Thursday Friday 26 12 29 10 15 32 18 19 15 32 37 27 16 25

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Statisticsmidsize mobile carrier keeps records of complaints received from its customers Complaints for last month are listed in the following table What percent of th mplaints are due to the categories Long customer service wait times or Poor coverage Round your answer to two decimal places if necessary Customer Complaints Type of Complaint Poor coverage Too expensive Extra data usage charges Long customer service wait times Poor tech support Incorrect billing Insurance doesn t cover loss theft Frequently drops calls Frequency 118 99 87 92 106 89 43 156

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StatisticsDryer Microwave Dishwasher Vashing Machine Dishwasher Washing Machine Dishwasher Dryer Microwave Refrigerator Refrigerator Dryer Microwave Dishwasher Washing Machine Dryer Microwave Dishwasher O nominal qualitative O ordinal qualitative Dryer Refrigerator Dr Micro Dishw Washing Dishwa

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StatisticsThe following data represent the prices in dollars of general admission tickets for the last 18 concerts at one venue Use the given data to determine the stems for this stem and leaf plot Answer Stem 71 48 60 57 47 71 61 68 68 44 73 49 78 43 72 52 45 75 Ticket Prices in Dollars Leaves Copy Data Tables Keypad Keyboard Shortcuts

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StatisticsThe following data represent the times in minutes required for 18 co workers to commute to work Determine the leaves for the given data points in the range 20 to 29 for this stem and leaf plot Answer 48 42 31 29 41 22 38 38 21 39 22 48 22 12 34 32 23 28 Selecting a stem will display the leaves necessary to complete the answer Not all boxes may be used Stem Commute Times in Minutes Leaves

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ProbabilityThe following data represent the number of oranges in hundreds which were sold by various grocery stores in the month of June Construct a dot plot for the given data Answer 9 2 7 15 2 4 10 6 7 4 13 7 8 10 6 15 Copy Data Tables Keypad Keyboard Shortcuts Select any value to see the controls for increasing or decreasing the frequency Use the up and down arrows or drag the slider to change the number of dots

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StatisticsThe following histogram shows the results of a personality questionnaire given to people applying for a customer service position Use this histogram to answer the questions 35 T Frequency 30 25 20 15 10 5 0 Class 1 3 29 Personality Questionnaire 10 Class 2 23 Class 3 17 24 Scores Step 1 of 5 Identify the class containing the smallest number of scores 1 2 3 4 5 or 6 17 Class 4 6 31 Class 5 38 Class 6 22 45 M

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Statisticse following histogram shows the results of a personality questionnaire given to people applying for a customer service position Use this histogram to answer the estions 35 30 25 Frequency 20 5 10 5 0 Class 1 3 7 Personality Questionnaire 8 Class 2 14 Class 3 13 18 Scores Step 1 of 5 Identify the class containing the smallest number of scores 1 2 3 4 5 or 6 26 Class 4 18 23 Class 5 29 28 Class 6 22 33 Meeting v

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StatisticsThe following stem and leaf plot represents the distribution of weights for a group of people Stem 12 13 14 15 16 17 18 19 20 2 3 3 7 2 5 6 1 3 1 4 6 7 1 3 4 9 3 1 1 5 7 Leaves 4 5 9 6 6 5 6 6 6 6 7 8 3 7 7 6 8 8 Key 1212 122 pounds 8

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Statisticshe following stem and leaf plot represents the distribution of weights for a group of people Stem 12 13 14 15 16 17 18 19 20 Step 1 of 3 What is the weight of the lightest person in the group Leaves 2 3 3 4 6 1 1 7 2 5 6 1 3 6 3 5 5 6 8 7 9 5 6 14 6 6 6 6 7 7 8 1 3 3 4 9 7 7 8 Key 12 12 122 pounds 8

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Statisticsc The agent observed 6 out of 12 business travelers who checked baggage She would like to know if this outcome provides convincing evidence that greater than 25 of business travelers check baggage To help answer this question we want to perform a simulation to estimate the probability that 6 or more out of 12 business travelers will check baggage Describe how to use a random number generator to perform one repetition of the simulation To determine if these data provide convincing evidence that more than 25 of business travelers check baggage 100 simulated samples of 12 business travelers were selected assuming that 25 check baggage The dotplot shows the number of business travelers in each simulated sample that check baggage

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StatisticsFrequency 24 20 16 12 8 4 0 70 5 7 75 5 Prealgebra Exam Scores 20 80 5 8 85 5 Scores 17 90 5 14 95 5 5 100 5

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StatisticsSuppose that for a certain experiment P A 0 6 and P B 0 3 If A and B are independent events find P A and B 0 90 O 0 30 0 18 0 50

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Statistics05 26 5 es Amazon Prime is a 119 per year service that gives the company s customers free two day shipping and discounted rates on overnight delivery Prime customers also get other perks such as free e books The accompanying table shows a portion of the annual expenditures in for 200 Prime customers Customer 1 2 1 200 Expenditure 1272 1089 1390 Expenditures 400 x 700 700 x 1000 1000 x 1300 1300 x 1600 1600 x 1900 1900 x 2200 picture Click here for the Excel Data File a 1 Construct the frequency and the relative frequency distribution for Expenditures Round relative frequency to 2 decimal places Check my work Frequency Relative Frequency