Final answer:
The range of f(x) = -6.2% is simply -6.2% itself as it's a constant value. For a normal distribution with a mean of 50 and standard deviation of 6, the range for about 68, 95, and 99.7 percent of the data lies within one (44 to 56), two (38 to 62), and three (32 to 68) standard deviations from the mean, respectively.
Step-by-step explanation:
The range of f(x) = -6.2% is not directly applicable because the function presented as f(x) = -6.2% is a constant function with only one output value, which is -6.2%. Therefore, the range consists of the single value -6.2%. However, if we are referring to the range of a normal distribution, such as X~ N(50, 6), we can calculate the range for different percentages of the data.
For 68 percent of the data, the range is between one standard deviation of the mean. Since the mean is 50 and the standard deviation is 6, about 68 percent of the x values lie between 44 (50 - 6) and 56 (50 + 6).
For 95 percent of the data, which is within two standard deviations, the x values lie between 38 (50 - 12) and 62 (50 + 12). And for 99.7 percent of the data, which is within three standard deviations, the x values lie between 32 (50 - 18) and 68 (50 + 18).