The National Health Survey uses household interviews to describe the health-related habits of U. S. adults. From these interviews they estimate population parameters associated with behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all U. S. adults. In the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16. We randomly select a sample of 100 smokers and calculate the proportion who started smoking before the age of 16. Required:
a. Based on your simulation, what is the average amount of error you expect to see in the sample proportions in this situation?
b. What is the margin of error based on 2 standard deviations?
c. Suppose we select a random sample of 100 smokers. We find that 20 started smoking before the age of 16 (20 out of 100 is 20%). Would a sample proportion of 20% be highly unlikely if the population proportion is 30%? How do you know?

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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