Final answer:
Using the Empirical Rule, approximately 95% of data values in a normal distribution lie within two standard deviations of the mean. With a mean of 80 and a standard deviation of 7, the range of 66 to 94 encompasses data within one standard deviation below to two standard deviations above the mean. Thus, approximately 0.95 times the total number of data values, or 0.95w, would fall within this range.
Step-by-step explanation:
To approximate the number of data values that will fall in the range between 66 and 94, given that the data set described is normally distributed with a mean of 80 and a standard deviation of 7, we can use the Empirical Rule. The Empirical Rule states that for a normal distribution, about 68% of data lies within one standard deviation (σ), about 95% within two standard deviations (2σ), and about 99.7% within three standard deviations (3σ). In this case, 66 is one deviation below the mean (80 - 7 = 73) and 94 is two deviations above the mean (80 + 2(7) = 94).
Since 66 is within the first standard deviation and 94 is within the second standard deviation, we look at the percentage of data within one and two standard deviations of the mean: approximately 95% of the data values fall within this range according to the Empirical Rule. If we have a total of w data values, to find the number of data values within the range 66 to 94, we multiply w by 95% (or 0.95).
Therefore, in this case, we expect about 0.95w data values to fall between 66 and 94.