Concept explainers
Life Expectancy The following table shown men’s and women’s life expectancy at birth (in years) for selected birth years in United States: (Data from: U.S. Center for National Health Statistics.)
Life Expectancy
Birth Year Men Women
1970 67.1 74.7
1975 68.8 76.6
1980 70.0 77.4
1985 71.1 78.2
1990 71.8 78.8
1995 72.5 78.9
2000 74.1 79.3
2005 75.0 80.1
2010 76.2 81.0
2015 77.1 81.7
Find the least-squares regression line for the men’s data, with
Find the least-squares regression line for the women’s data, with
Suppose life expectancy continues to increase as predicted by the equations in parts (a) and (b). Will men’s life expectancy ever be higher than the women’s? If so, in what birth year will this occur?
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Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
- Cigarette Smokers The following table gives a recent estimate in millions of the smoking status among persons 25 years of the age and over their highest level of education. Source: National health interview survey. Education Current smoker Former smoker Non smoker Total Less than a high school diploma 7.90 6.66 14.12 28.68 High school diploma or GED 14.38 13.09 25.70 53.17 Some collage 12.41 13.55 28.65 54.61 Bachelors degree or higher 4.97 12.87 38.34 56.18 Total 39.66 46.17 106.81 192.64 a. Find the probability that a person is a current smoker. b. Find a probability that a person has less than a high school diploma. c. Find a probability that a person is a current smoker and has less than a high school diploma. d. Find the probability that a person is a current smoker, given that the person has less than a high school diploma. e. Are the events current smoker and less than a high school diploma independent events?arrow_forwardOil ProductionThe following table shows the amount of crude oil in billions of barrels produced in the United States in recent years. Source: U.S. Energy Information Administration. Year Crude Oil Produced 2002 2.097 2003 2.060 2004 1.989 2005 1.893 2006 1.857 2007 1.853 2008 1.830 2009 1.954 2010 2.000 2011 2.063 2012 2.377 In this exercise we are interested in the total amount of crude oil produced over the 10-year period from mid-2002 to mid-2012, using the data for the 11 years above. One approach is to sum up the numbers in the second column, but only count half of the first and last numbers. Give the answer to this calculation. Approximate the amount of crude oil produced over the 10-year period 2002-2012 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part a. This is also equivalent to a formula known as the trapezoidal rule, discussed in the next chapter. If your calculator has a cubic regression feature, find the best-fitting cubic function for these data, letting t=0 correspond to 2000. Then integrate this equation over the interval [2.12] to estimate the amount of crude oil produced over this time period. Compare with your answer to part a.arrow_forward
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