Empirical Rule

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

Question

Empirical Rule

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

BlackTom AI · Accepted Answer

The question presents an Empirical Rule problem and asks for the numerical value of the lower bound (LB) of the interval, to be entered as a whole number.

First, recall what the Empirical Rule (68-95-99.7) implies for a normal distribution: the interval that captures about 99.7% of the data is centered at the mean μ and extends from μ − 3σ to μ + 3σ, where σ is the standard deviation. Therefore, the lower bound of this widely used interval is given by LB = μ − 3σ.

Since the problem asks for a numerical LB and provides no answer choices to evaluate, you’d typically need the mean and the standard deviation from the data or from a prior part of the question to compute μ − 3σ. If those values were given (e.g., you were told μ and σ), you would simply perform the subtraction and round as needed to a whole number. In some contexts, the problem might have already condensed μ − 3σ to a value like −3, which would be the LB in that specific setup.

Common misconceptions to watch for:
- Confusing the lower bound with the mean μ or with −σ or with a z-score of −3. The LB is not μ itself, nor is it simply −3 unless μ and σ are such that μ − 3σ = −3.
- Using the wrong interval width. The 68-95-99.7 rule uses μ ± 1σ and μ ± 2σ for narrower intervals, but the full 99.7% interval uses μ ± 3σ, so the LB would be μ − 3σ.
- Forgetting to ensure the value is a whole number when the instruction requires a whole number; if μ − 3σ results in a decimal, you would typically round according to the problem’s rounding policy (though the prompt says enter as a whole number, which implies the target value is already an integer).

If you were provided with μ and σ elsewhere in the problem and computed LB as μ − 3σ, you would substitute those numbers and simplify to a single integer, matching the required format. If instead the problem statement already states that LB equals −3, that would reflect the specific μ and σ values given in that setup.

STAT_008_A01_25U Lab #10

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

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