Empirical Rule

Q3 b) What is the numerical value for the upper bound (UB) of the interval? Enter your answer as a whole number.

Question

Empirical Rule

Q3 b) What is the numerical value for the upper bound (UB) of the interval? Enter your answer as a whole number.

BlackTom AI · Accepted Answer

The question presents: Empirical Rule, Q3 b) What is the numerical value for the upper bound (UB) of the interval? Enter your answer as a whole number.

First, I note there are no answer options provided to analyze, so I cannot compare multiple choices. In such cases, it helps to recall what the Empirical Rule (68-95-99.7 rule) implies for a normal distribution.

- The empirical rule describes intervals around the mean in terms of standard deviations (σ):
  - About 68% of data lie within mu ± 1σ,
  - About 95% lie within mu ± 2σ,
  - About 99.7% lie within mu ± 3σ.

If the problem asks for the numerical value for the upper bound (UB) of the interval in standardized terms, the UB corresponds to mu + kσ, where k is 1, 2, or 3 depending on which interval is being referenced. For the common acceptance that the “upper bound” of the 99.7% interval is mu + 3σ, the numeric multiplier on σ is 3, which is often the value sought when one is asked for a numerical bound in terms of standard deviations.

However, since the prompt requests a numerical value and provides no data (mu or σ) and offers no options to inspect, the typical answer style would be to report the multiplier 3 if the question intends the UB in terms of standard deviation units (i.e., the 3σ upper bound). If the question instead required an absolute numeric bound given specific mu and σ values, that information would be necessary to compute an actual numeric UB.

In summary:
- The empirical rule uses bounds at 1σ, 2σ, and 3σ from the mean.
- The standard numeric multiplier for the upper bound of the widest common interval (the 99.7% interval) is 3.
- Without mu and σ values or explicit instruction about what the numeric value should represent (multiple of σ vs. an absolute value), the safest interpretation of a requested numeric UB that aligns with the common empirical-rule bound is the number 3.

If you have mu and σ values or if the problem specifies which interval (68%, 95%, or 99.7%) to use, I can compute the exact numerical UB accordingly with those parameters.

STAT_008_A01_25U Lab #10

Empirical Rule Q3 b) What is the numerical value for the upper bound (UB) of the interval? Enter your answer as a whole number.

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