Processors usually preserve cucumbers by fermenting them in a low-salt brine (6% to 9%

Chapter 11, Problem 11.12

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Processors usually preserve cucumbers by fermenting them in a low-salt brine (6% to 9% sodium chloride) and then storing them in a high-salt brine until they are used by processors to produce various types of pickles. The high-salt brine is needed to retard softening of the pickles and to prevent freezing when they are stored outside in northern climates. Data showing the reduction in firmness of pickles stored over time in a low-salt brine (2% to 3%) are given in the accompanying table.3 Weeks (x) in Storage at 72F 0 4 14 32 52 Firmness (y) in pounds 19.8 16.5 12.8 8.1 7.5 a Fit a least-squares line to the data. b As a check on your calculations, plot the five data points and graph the line. Does the line appear to provide a good fit to the data points? c Use the least-squares line to estimate the mean firmness of pickles stored for 20 weeks.