# Statistics Questions

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The Graduate Management Admission Test GMAT is a standardized exam used by many universities as part of the assessment for admission to graduate study in busines The average GMAT score is 547 t Assume that GMAT scores are bell shaped with a standard deviation of 100 a What percentage of GMAT scores are 647 or higher b What percentage of GMAT scores are 747 or higher c What percentage of GMAT scores are between 447 and 547 d What percentage of GMAT scores are between 447 and 747 6 24 C M
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Consider a sample with data values of 10 20 14 12 and 11 Compute the range and interquartile range range interquartile range
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Consider a sample with data values of 10 20 12 17 and 16 Compute the variance and standard deviation sample variance sample standard deviation
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Consider a sample with data values of 20 26 28 15 30 34 24 and 26 Compute the range Compute the interquartile range Compute the sample variance Round your answer to two decimal places Compute the sample standard deviation Round your answer to two decimal places
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Five observations taken for two variables follow 20 18 16 14 12 10 8 6 4 2 0 O 0 a Develop a scatter diagram for these data y y 20 X 6 Y 7 8 18 16 14 12 10 8 6 4 2 11 5 15 21 27 7 17 11 10 15 20 25 30 X y 20 18 16 14 12 10 8 6 4 2 0 5 10 15 20 25 X 30 O 20 y 18 16 14 12 10 8 6 4 2 0 0 5 10 15 20 2
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80 70 60 50 40 30 20 10 0 0 80 70 60 50 40 30 20 10 Develop a scatter diagram with x on the horizontal axis y 0 11 3 5 Y 50 60 40 60 30 16 10 10 15 15 20 X X 20 y 80 70 60 50 40 30 20 10 0 0 y 80 70 60 50 40 30 20 10 0 0 5 10 10 15 15
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Consider a sample with data values of 10 20 21 12 18 and 15 Compute the mean and median mean median
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Consider a sample with data values of 52 54 70 58 64 57 52 69 57 68 and 52 Compute the mean Round your answer to two decimal places Compute the median Compute the mode
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You may need to use the appropriate technology to answer this question To study the effect of temperature on yield in a chemical process five batches were produced at each of three temperature levels The results follow Source of Variation 50 C 60 C 70 C Treatments Error Total 34 Temperature 23 36 38 29 29 31 35 22 28 24 29 Construct an analysis of variance table Round your values for MSE and F to two decimal places and your p value to four decimal places 27 29 36 Sum Degrees of Squares of Freedom Mean Square jue hunsthases F p value Use a 0 05 level of significance to test whether the temperature level has an effect on the mean yield of the process
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You may need to use the appropriate technology to answer this question A company manufactures printers and fax machines at plants located in Atlanta Dallas and Seattle To measure how much employees at these plants know about quality management a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination The examination scores for these 18 employees are shown in the following table The sample means sample variances and sample standard deviations for each group are also provided Managers want to use these data to test the hypothesis that the mean examination score is the same for all three plants Sample mean Treatments Error Sample variance Sample standard deviation Plant 1 Atlanta 86 76 82 75 72 89 80 45 2 6 72 Plant 2 Dallas 72 74 73 74 68 83 74 24 4 4 94 Plant 3 Seattle Degrees of Freedom 58 64 62 69 75 62 65 Set up the ANOVA table for these data Round your values for MSE and F to two decimal places and your p value to four decimal places Sum Source of Variation of Squares 36 8 6 07 Mean Square F p value
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j 1 The given data are below 7 x j 1 SSTR k n x 7 2 Sample mean Sample variance XatXBtxc k 29 45 37 Treatment Treatment A B 33 29 30 25 28 29 8 50 44 42 45 46 48 45 5 00 Treatment C 34 36 There are 3 treatments so k Each treatment has 5 observations so nA nB nc The total number of observations is n A 8 ne Since each treatment has the same number of observations the overall sample mean for the k sample means is found as follows Find the overall sample mean 36 37 42 37 9 00
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f xxx x y for 2 x 6 02 y 24 Solve P x 2 2 X and
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f x x x y for 22x26 02 y 24 Find Marginal distribution and probability X of
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f x x x y for 22x26 02424 Solve Cor x y and
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f x y x y for 22x26 02 y 24 P X 1 an
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Determine the value of c such that the function f x y cx y for 2 x 6 and 0 y 4 satisfies the properties of a joint probability density function Determine the following a Marginal probability distribution of X b P Y 1 c P X 2 Y 2 d P 2 5 X 4 5 Y 3 e E X f Var Y g Cov X Y h Cor X Y i Are X and Y independent Why or why not
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You are playing a game where you must roll two 4 sided dice each die can yield a value of 1 2 3 or 4 The goal is to obtain a score of at least 6 You initially roll both dice and are allowed to reroll one of them the other die value must be kept For example if you roll the dice and obtain the results of 1 and 3 you will want to reroll the die with a value of 1 to try to get a higher value You do not need to roll again if your initial roll obtains a combined score of at least 6 Find the following a The probability that you succeed without needing to reroll the dice the odds that the values sum to at least 6 when you first roll both dice b In what scenario would you be unable to succeed after your first roll think what values must be present on both dice in which rerolling one of them will never allow them to sum to at least 6 What is the likelihood of this c You discover that one of the die is rigged and will always roll a 2 Given this information what is the chance of each of the following i You succeed in any given turn your chance to obtain a total score of 6 or greater given the initial rules ii After 5 tries you succeed at least 3 times iii You succeed exactly 5 times after 7 tries
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ou have noticed some variation in the amount of rice provided in your usual order of General so s Chicken You ask the store manager about this issue and they confirm that the reparation of your order isn t directly measured In each order you are supposed to be given cup of rice which should be 250 grams if measured exactly Based on data provided by the manager you find that the true amount of rice given follows a normal distribution with an verage of 252 grams and a standard deviation of 1 5 grams Given this information a How often will you receive less rice than you pay for less than 250 grams b If your rice container can only fit 256 grams how often will it overflow when your cook is filling it c If both these situations are considered as errors how many errors should you expect after ordering 10 times
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2 LO 5 4 4 5 3 3 5 5 3 1 4 st 3 4 4 LO 5 3 5 5 2 5 5 5 2
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The following stem and leaf plot was constructed using the number of telephone calls made by 20 executives during a randomly selected week Make a list of the data represented by the plot from smallest to largest Stems Leaves 1 2 12588 02246894 3 137 4 5 19 389
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Briefly explain the error in the construction of the ogive below which illustrates the average quantitative GRE scores to the top 30 graduate schools of engineering Cumulative Frequency 2 25 20 15 10 S 0 744 756 770 777 784
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Let s assume that the function f x y c 3x 2y represents a joint probability mass function for x 1 3 5 and y 2 4 6 Determine a The value of c b P X 3 5 Y 3 c P X 3 d E X e V Y f Marginal probability distribution of X g Are X and Y independent Why or why not
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n average a certain intersection results in an average of 1 3 traffic accidents pe etermine the probability of the following situations for any given week a Exactly I accident occurs b No more than 2 accidents occur c At least 3 accidents occur
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Professor for one of your classes takes random sample of 100 student grades and obtains a mple mean of 85 with a sample standard deviation of 6 7 a Construct a 95 confidence interval for the true average grade b If this professor guessed that the standard deviation for grades overall is 10 what sample size would be required to obtain an interval width of 3 for a confidence level of 90
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1 ok int rint erences Hui is currently considering investing in municipal bonds that earn 8 40 percent interest or in taxable bonds issued by the Coca Cola Company that pay 11 20 percent Required a If Hui s tax rate is 22 percent which bond should he choose b Which bond should he choose if his tax rate is 32 percent c At what tax rate would he be indifferent between the bonds d What strategy is this decision based upon Complete this question by entering your answers in the tabs below Required A Required B Required C Required D If Hui s tax rate is 22 percent which bond should he choose
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Forty plasma TVs were tested and the number of watts per hour they used recorded Given that the lowest value is 429 find the class limits to be used in the construction of a frequency distribution for the data with 6 classes and a class width of w 13 Begin the first class with the smallest data value given above and write the limits for the classes in the table provided in the answer box below
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4 2 2 5 In example of lecture 5 Sec 2 2 An enterprising man proposes a game let the player throw a die Let the reward becomes Z u X X a Find the pmf of Z say h z b Find E Z c How much on average can the enterprising man expect to win on each play from players if he charges 10 dollars per play
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Assume that the U S Mint manufactures dollar coins so that the standard deviation is 0 0390 g The accompanying list contains weights grams of dollar coins manufactured with a new process designed to decrease the standard deviation so that it is less than 0 0390 g This sample has these summary statistics n 16 x 8 066 g s 0 02 g A 0 05 significance level is used to test the claim that the sample is from a population with a standard deviation less than 0 0390 g The null and alternative hypotheses are Ho o 0 0390 g and H o 0 0390 g For this sample data we get a P value of 0 0099 when testing the claim that o 0 0390 g Complete parts a through c a What should we conclude about the null hypothesis 4 O A Accept the null hypothesis OB Fail to reject the null hypothesis OC Fail to accept the null hypothesis OD Reject the null hypothesis
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Use the accompanying 200 Los Angeles commute times to test the claim that the mean Los Angeles commute time is less than 32 minutes Assume that a simple random sample has been selected Use a 0 10 significance level Compare the sample mean to the claimed mean of 32 minutes Is the difference between those two values statistically significant Click the icon to view the Los Angeles commute times Identify the null and alternative hypotheses Ho 32 H 32 Type integers or decimals Do not round Identify the test statistic Round to two decimal places as needed 4
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adults in a recent year Construct a frequency distribution that has seven classes Adapted the out of pocket prescription medicine expenses in dollars for 30 U S from Health United States 2015 Create a frequency distribution for this data 200 239 155 252 384 165 296 405 303 400 307 241 256 315 330 317 352 266 276 345 238 306 290 271 345 312 293 195 168 342 Total Class 3 Tally Frequency f Relative Frequency
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In the following problem check that it is appropriate to use the normal approximation to the binomial Then use the normal distribution to estimate the requested probabilities Ocean fishing for billfish is very popular in a certain region of Mexico In this region about 39 of strikes while trolling resulted a catch Suppose that on a given day a fleet of fishing boats got a total of 28 strikes Find the following probabilities Round you answers to four decimal places USE SALT a 12 or fewer fish were caught b 5 or more fish were caught c between 5 and 12 fish were caught
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A survey about social media reported that 77 of B2B marketers marketers that focus primarily on attracting businesses plan to increase their use of social media as compared to 56 of B2C marketers marketers that primarily target consumers The survey was based on 1 426 B2B marketers and 1 618 B2C marketers The accompanying table summarizes the results Complete parts a through d below Click the icon to view the contingency table about social media use and marketers a What is the probability that a randomly selected respondent plans to increase use of social media Round to three decimal places as needed U P O DE E SE ELEV
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2 Ms Lioktsis has opened up multiple bags of M M chocolates and counted how many chocolates are in each The amounts are shown in the box below 7 marks 58 58 52 54 55 49 34 34 34 35 42 41 35 39 39 37 42 42 43 43 44 45 45 45 46 58 a Organize the data into the frequency table Be sure to show all your work Interval 30 34 35 39 40 44 45 49 50 54 55 59 Total Interval Frequency Sum Midpoint Cumulative Freq Frequency x mean
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S Name the x coordinate of one solution to the system of equations 2
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A firework is shot straight up into the air with an initial velocity of 500 feet per second from 5 feet off the ground The function modeling the path of the firework is h t 16t 500 5 A At what time will the firework hit the ground numerical answer only round to the nearest tenth 31 3 B Write the inequality that represents when the firework is below 2500 feet Enter your answer here 16 500 5 2500 C Solve the inequality you wrote in B and enter your answer here round to the nearest tenth 6 2 t 31 3
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Determine the number of solutions for each of the graphs DRAG DROP THE ANSWER One Solution Two Solutions No Solution
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What are the solution s to the system of equations Select all that apply 2 5 25 D 1 0 10 3 75 325
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Solve the inequality algebraically Report the solution in interval notation 2 7 12 2003 4
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The height in feet of a football that is kicked can be modeled by the function 16a 64a where is the time in seconds after it is kicked for what time is the ball at or above a height of 48 feet above the ground
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7 The height in feet of a football that is kicked can be modeled by the function f a 16z 6z where is the time in seconds after it is kicked For what time s is the ball at or above a height of 48 feet above the ground
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II f x 2x 8m mx k 3x 8x 2k x 2 2 x 2 x 2
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