Question;NAME:If you choose to complete the following project, it will replace the lowest exam grade thatyou have received on exams one through three. However, if the grade you receive on thisproject is lower than your lowest exam grade, I will not count the project. When writing upyour answers, please include and show your work that was needed to answer each questionon separate paper. You will not receive credit for a question if the necessary work is notprovided. Please write your final answers on the answer sheet provided. I will not acceptany projects written up on this handout. The due date is May 9, 2013 at the beginning ofclass. Any projects turned in after this time will not be accepted. Good luck!1.The following table provides the number of miles Professor Rojas ran per day for a sample of 50days from this past summer:3.03.725.084.015.03.743.763.734.6220.127.116.113.393.795.04.05.04.03.723.733.374.013.358.025.013.724.563.683.55.04.925.05.04.04.04.624.64.04.63.3210.015.05.018.024.974.04.5713.194.015.01a. Construct a frequency distribution table using 6 classes (include class,b.c.d.e.f.g.frequency and class boundaries)Construct a histogramDetermine the mean, median, and mode of the number of miles ran per day.Determine the standard deviation of the number of miles ran per day.Interpret your answer to part d.Does there seem to be any outliers? Explain.Which measure(s) of central tendency, if any, do you think best illustrates thenumber of miles Professor Rojas runs per day?2.Suppose you buy a new car whose advertised mileage is 25 miles per gallon (mpg). After drivingyour car for several months, you find that its mileage is 21.4 mpg. You call the manufacturer andlearn that the standard deviation of gas mileages for all cars of the model you bought is 1.15 mpg.Assume mileage follows a bell-shaped distribution.a. Find the z-score for the gas mileage of your car.b. Use the z-score to explain the relative standing of your cars gas mileage.c. Does it appear that your car is getting unusually low gas mileage? Explain your answer.3.Explain what is wrong with the following argument: When a balanced coin is tossed twice, thetotal number of heads obtained can be 0, 1, or 2. This gives three possibilities. So, the probabilityof getting two heads is 1/3.4.Consider the random variable X, the grade level of a secondary-school student selected at random.Its probability distribution is as follows.xP(x)a.b.c.d.9101112.301.263.232.204Find the mean grade level of a secondary student.Calculate the standard deviation.What is the probability that a secondary student selected at random is in 11th grade?What is the probability that the grade level of a secondary student selected at random iswithin one standard deviation of the mean grade level?5.Studies show that 60% of U.S. families use physical aggression to resolve conflict. If 100 familiesare selected at random, find the probability that the proportion of families that use physicalaggression to resolve conflict will bea. Less than 55%.b. Between 53% and 64%,c. What is the sample proportion that cuts of the top 15% of the sample proportions?6.The annual wages, excluding board, of U.S. farm laborers in 1926 were normally distributed witha mean of $586 and a standard deviation of $97. In 1926, what percentage of U.S. farm laborershad an annual wage ofa. Between $500 and $700?b. At least $400?c. What minimum annual wage would a farmer selected at random have to earn in order tobe in the top 10%?d. What annual wage would a farmer selected at random have to earn in order to be at the40th percentile?7.Due to an attractive labor market, a great music scene, and other benefits, rents for apartments inAustin, Texas, have increased dramatically in the past decade. Suppose rents for apartments inAustin are normally distributed with a mean monthly rent for a 1000 sq. ft. apartment of $880with a standard deviation of $150. If 100 apartments in Austin are selected at random, what is theprobability that the mean rent will bea. Greater than $900?b. Between $850 and $930?c. What is the sample mean that cuts off the bottom 5% of the sample means?8.The International Shark Attack File (ISAF), maintained by the Florida Museum of Natural Historyand The American Elasmobranch Society, compiles shark attack records throughout the world. Ofinterest to many scientists is whether shark attacks are occurring more frequently due to anincreased human presence along the coastline. The following table shows data for a randomsample of records from the ISAF on the number of unprovoked shark attacks (y) and the humanpopulation size (x), in tens of thousands, where the attacks occurred.x2043 507095 105125600 200 25y639102045114171a. Graph the above data and state the apparent relationship between human population sizeand number of shark attacks (you do not need to provide the graph on the answer key).Determine the correlation coefficient.Interpret the correlation coefficient.Determine the coefficient of determination.Interpret the coefficient of determination.Determine the regression equation.What does the slope of the regression line represent in terms of human population sizeand number of shark attacks?h. Use the regression equation to predict the number of shark attacks for a humanpopulation size of 600,000.b.c.d.e.f.g.9.A certain exam follows a normal distribution with = 77 and population standard deviation equalto. If an exam grade of 85 cuts off the top 15% of the distribution, then find the populationstandard deviation.10. The Gallup Organization conducts annual national surveys on home gardening. Results arepublished by the National Association for Gardening in National Gardening Survey. A randomsample is taken of 25 households with vegetable gardens. The mean size of their gardens is 643 sqft with a standard deviation of 247 sq. ft.a. Determine a 90% confidence interval for the mean size,, of all household vegetablegardens in the United States.b. Interpret your answer from part (a).11. As reported in Library Journal by the R. R. Bowker Company of New York, the mean annualsubscription rate of law periodicals was $138.78 in 1998. A sample of this years law periodicalsyielded the following subscription rates to the nearest dollar.147159169163155165161179160164172171a. Determine a 95% confidence interval for this years mean annual subscription rate,, forall law periodicals.b. Does your result from part (a) suggest a difference in the mean annual subscription ratefrom that in 1998? Explain your answer.
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