The Empirical Rule states that for a bell-shaped distribution, approximately 95 percent of data should lie within:

Question

BlackTom AI · Accepted Answer

Consider the prompt: The Empirical Rule states that for a bell-shaped distribution, approximately 95 percent of data should lie within:

Option A: 'three standard deviations from either side of the mean.' This corresponds to about 99.7% of data under a normal distribution, not 95%. So this overestimates the interval.

Option B: 'one standard deviation from either side of the mean.' This captures roughly 68% of data in a normal distribution, not the 95% target, so it underestimates the spread.

Option C: 'two standard deviations from either side of the mean.' This is the classic 95% interval described by the Empirical Rule (also known as the 68-95-99.7 rule). It accurately identifies the central region that includes about 95% of data in a bell-shaped distribution.

Option D: 'four standard deviations from either side of the mean.' This would enclose an extremely large portion of data, well over 99% for a normal distribution, and is not the standard 95% interval described by the rule.

In sum, the intended 95% coverage corresponds to the interval spanning two standard deviations on either side of the mean, while the other options misstate the commonly cited percentages for normal distributions. The key diagnostic is linking 95% to the span of two standard deviations around the mean, rather than one, three, or four.

The Empirical Rule states that for a bell-shaped distribution, approximately 95 percent of data should lie within: Single choice

Similar Questions

Suppose a population has probability distribution with a mean 𝜇 and a standard deviation 𝜎 . If a random sample of 100 measurements are taken from this population, you would expect very few of them to fall within 3 standard deviations of the mean. c07.p066.q001

According to the Empirical Rule, the probability that a selected dog of this breed weighs more than 161 pounds is about

Empirical Rule Q3 d) Find P(LB < Z< UB). Enter your answer to 4 decimal places.

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

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

Empirical Rule Q2 d) Find P(LB < Z< UB). Enter your answer to 4 decimal places.

Empirical Rule Q2 b) What is the numerical value for the upper bound (UB) of the interval? Enter your answer as a whole number.

Empirical Rule Q2 a) What is the numerical value for the lower bound (LB) of the interval? Enter your answer as a whole number.

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler