Final answer:
To determine the 68 percent and 95 percent range for y-values, the mean and standard deviation of the data must be calculated. The given best-fit line equation (ŷ = -173.51 + 4.83x) aids in predicting y from x. The data is analyzed statistically with the use of a regression line.
Step-by-step explanation:
To answer the question about the ending values of x and y, we need to look at the data provided, including the final exam scores for math (x) and history (y), and analyze it statistically.
About 68 percent of the y values lie within one standard deviation of the mean. Similarly, about 95 percent of y values fall within two standard deviations of the mean. This is based on the empirical rule, which is applicable for normal distributions. To find these values specifically, we would calculate the mean and standard deviation of the y-values and apply the empirical rule. The exact values that 68 percent and 95 percent of the y-values lie between are not provided here, so we cannot specify them without further calculation.
The equation of the best-fit line is given by ŷ = -173.51 + 4.83x. This allows us to predict the y value (final exam score) based on the x value (third exam score).
The dependent variable y is determined by the independent variable x, and the relationship between them is best visualized through a regression line or best-fit line.