Statistics and probability:-
Determine the range of the homework data from. The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan's Intermediate Algebra course spent on the homework from Factoring Polynomials. 48 88 57 109 111 193 71 83 Source: MyMathLab(a) Determine the standard deviation of the homework data from The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan's Intermediate Algebra course spent on the homework from Factoring Polynomials. 48 57 109 111 71 83 Source: MyMathLab (b) By hand, determine and interpret the interquartile range of the homework data from Problem. The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan's Intermediate Algebra course spent on the homework from Section, Factoring Polynomials. 88 57 109 11 93 71 83 Source: MyMathLab (c) Which of these two measures of dispersion is resistant? Why? Problem The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan's Intermediate Algebra course spent on the homework from Section, Factoring Polynomials. 83 57 109 111 93 71 83 Source: MyMathLab (a) Determine the mean amount of time spent doing Section homework. (b) Determine the median amount of time spent doing Section homework. (c) Suppose the observation 109 minutes is incorrectly recorded as 1009 minutes. Recompute the mean and the median. What do you notice? What property of the median does this illustrate?In a random sample of 250 toner cartridges, the mean number of pages a toner cartridge can print is 4302 and the standard deviation is 340. (a) Suppose a histogram of the data indicates that the sample data follow a bell-shaped distribution. According to the Empirical_Rule, 09.7% of toner cartridges will print between and pages. (b) Assuming that the distribution of the data are bell shaped, determine the percentage of toner cartridges whose print total is between 3622 and 4082 pages. (c) If the company that manufactures the toner cartridges guarantees to replace any cartridge that does not print at least 3622 pages, what percent of cartridges can the firm expect to be responsible for replacing, according to the Empirical Rule? (d) Use Chebyshev's inequality to determine the minimum percentage of toner cartridges with a page count within 1.5 standard deviations of the mean. (e) Use Chebyshev's inequality to determine the minimum percentage of toner cartridges that print between 3282 and 5322 pages.The following data represent the length of time (in minutes) between eruptions of Old Faithful in Yellowstone National Park. Time (minutes) Frequency 40-49 50-59 44 80-69 23 70-79 80-89 107 90-99 11 100-109 (a) Approximate the mean length of time between eruptions. (b) Approximate the standard deviation length of time between eruptions.Travel Time to Work The frequency distribution listed in the table represents the travel time to work (in minutes) for a random sample of 895 U.S. adults. Travel Time (minutes) Frequency 0-9 125 10-19 271 20-29 186 30-39 121 40-49 54 50-50 82 80-60 43 70-79 20 80-80 13 Source: Based on data from the 2009 American Community Survey (a) Approximate the mean travel time to work for U.S. adults. (b) Approximate the standard deviation travel time to work for U.S. adults.Survival Rates Unfortunately, a friend of yours has been diagnosed with cancer. You obtain a histogram of the survival time (in months) of patients diagnosed with this form of cancer as shown in the figure. The median survival time for individuals with this form of cancer is 11 months, while the mean survival time is 69 months. What words of encouragement should you share with your friend from a statistical point of view? Survival Time of Patients Percent 10 120 160 Survival Time (months)Blood Alcohol Concentration Go to http://www.pearsonhighered.com/sullivanstats to obtain the data 3_1 35. The data represent the blood alcohol concentration (BAC), in percent, of a random sample of drivers involved in fatal car accidents. A BAC of 0 indicates that no alcohol was present. Draw a histogram of the data, describe the shape, and determine the mean and median BAC of drivers in fatal accidents. Which measure of central tendency better describes the typical BAC of drivers in fatal accidents? Explain.Sullivan Survey Go to http:/www.pearsonhighered.com/ sullivanstats and download the Sullivan Stats Surveyl data. The data represent the results of a survey conducted by the author. The column "Texts" represents the number of texts the individual sent for the month prior to the survey. Draw a relative frequency histogram and determine the mean and median number of texts for each gender. Make some general comments about the results.Trimmed Mean Another measure of central tendency is the trimmed mean. It is computed by determining the mean of a data set after deleting the smallest and largest observed values. Compute the trimmed mean for the data in. Problem Is the trimmed mean resistant? Explain. Problem M&Ms The following data represent the weights (in grams) of a simple random sample of 50 M&M plain candies. 0.87 0.88 0.82 0.90 0.90 0.84 0.84 0.91 0.94 0.86 0.86 0.86 0.88 0.87 0.89 0.91 0.86 0.87 0.93 0.88 0.83 0.95 0.87 0.93 10.91 0.85 0.91 0.91 0.86 0.89 0.87 0.84 0.88 0.88 0.89 0.79 0.82 0.83 0.90 0.88 0.84 0.93 0.81 0.90 0.88 0.92 0.85 0.84 0.84 0.86 Determine the shape of the distribution of weights of M&Ms by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes the weight of a plain M&M?You are negotiating a contract for the Players Association of the NBA. Which measure of central tendency will you use to support your claim that the average player's salary needs to be increased? Why? As the chief negotiator for the owners, which measure would you use to refute the claim made by the Players Association?Which histogram depicts a higher standard deviation? Justify your answe Frequency 40 44 48 52 56 60 10 Frequency 30 35 40 -45 50 55 60 65 70 75 (b)
