Ever since the start of the 21st century, life expectancy has steadily increased. The table below shows the life expectancy based on the year between 2000-2020. Year Life Expectancy (years) 2001 47 2002 50 2004 54 2006 60 2008 64 2010 68 2012 71 2014 73 2016 76 2018 78 2020 80 (a) Let x represent time in years starting with x = 1 for the year 2001. Using your calculator, find the logarithmic regression (LnReg) that models this situation. Call this equation L(x). Round to 3 decimal places. (b) According to the model L(x), what will be the life expectancy be in 2030? Round to the nearest year. (c) Using the model, algebraically determine what year the life expectancy will be 95 years old? Round the answer to the nearest year.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Ever since the start of the 21st century, life expectancy has steadily increased. The table below shows the life expectancy based on the year between 2000-2020.
Year Life Expectancy (years)
2001 47
2002 50
2004 54
2006 60
2008 64
2010 68
2012 71
2014 73
2016 76
2018 78
2020 80
(a) Let x represent time in years starting with x = 1 for the year 2001. Using your calculator, find the logarithmic regression (LnReg) that models this situation. Call this equation L(x). Round to 3 decimal places.
(b) According to the model L(x), what will be the life expectancy be in 2030? Round to the nearest year.
(c) Using the model, algebraically determine what year the life expectancy will be 95 years old? Round the answer to the nearest year.
Given information:
The table representing the life expectancy based on the year between 2000-2020 is:
Year Life Expectancy (years)
2001 47
2002 50
2004 54
2006 60
2008 64
2010 68
2012 71
2014 73
2016 76
2018 78
2020 80
It is required to obtain:
(a) the logarithmic regression equation L(x)
(b) the life expectancy in 2030 using the model
(c) the year in which life expectancy will be 95 years old.
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