Over time, according to records kept by the Environmental Protection Agency (found at www.epa.gov), recycling rates have increased from 10% of municipal solid waste generated in 1980 to 16% in 1990, to 29% in 2000, and to 34% in 2009. Meanwhile, disposal of waste to a landfill has decreased from 89% of the amount generated in 1980 to 54.3% of solid waste in 2009. The prediction equation (or least- squares prediction equation) for the percent of solid waste recycled by Americans is y = 0.932x - 1837 where y = percent of solid waste recycled and x is the year. (a) Graph these data (percent recycled vs. year), leaving room at both ends for past and future years. Draw the line given by the prediction equation on your graph also. (b) Is the slope positive or negative? What does the slope tell us about the rate of recycling over the past 30 years? (c) Use the prediction equation to determine the x-intercept. What does this value tell you? Use your graph to help you verify your answer by plotting this point. (d) During what year will recycling theoretically reach 50% according to this model? Plot this point on your graph. (e) Theoretically, will recycling ever reach 100%? Practically speaking, is that really possible?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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