Final answer:
The assertion that approximately 84 percent of people do higher than 1 standard deviation below the mean is false. According to the Empirical Rule for a symmetric bell-shaped distribution, about 68 percent of data is within one standard deviation of the mean, which implies that approximately 66 percent would be higher than 1 standard deviation below the mean.
Step-by-step explanation:
The student's question pertains to the Empirical Rule, which applies to a bell-shaped, symmetric distribution (typically the Normal or Gaussian distribution). According to this rule, approximately 68 percent of data falls within one standard deviation of the mean. Therefore, 84 percent of people doing higher than 1 standard deviation below the mean is false. Instead, if we consider one standard deviation below and above the mean, that covers approximately 68 percent of the data. However, if we consider only above one standard deviation below the mean to the mean itself, this would include roughly half of that 68 percent, or 34 percent. Therefore, the correct percent would be 100% - 34%, which is about 66 percent, not 84 percent.
It is important to differentiate between the Empirical Rule and rules that apply to any data set distribution, such as Chebyshev's Rule. With Chebyshev's Rule, we know that at least 75 percent of the data is within two standard deviations of the mean for any shaped distribution, which is less specific than the Empirical Rule for symmetric, bell-shaped distributions.