A researcher creates a scatter plot that displays the relationship between the number of years in business, , and the percentage of company business that is fair trade, . The researcher creates a line of best fit, , and wants to find the residuals for the companies that have been in business for 3 years. 1. Find the residuals for the two points representing companies that have been in business for 3 years, and .
2. Compare the residuals for the two companies who have been in business for 3 years. How are they different? How are they similar? What does the information about the residuals for the two companies tell you about their fair trade business?

many reason,

step-by-step explanation:

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irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.