Question 1

Which of the following best describes the 'range rule of thumb' for identifying significantly low or high values in a probability distribution?

Accepted Answer

Values are considered significantly low if they are less than or equal to $$\mu - 2\sigma$$, and significantly high if they are greater than or equal to $$\mu + 2\sigma.$$

Question 2

Suppose a random variable $$X$$ has mean $$\mu = 10$$ and standard deviation $$\sigma = 2. $$According to the range rule of thumb, which of the following values would be considered significantly high?

Accepted Answer

$$X = 14$$

Question 3

If $$\mu = 5$$ and $$\sigma = 1.5$$, what is the cutoff for significantly low values according to the range rule of thumb?

Accepted Answer

$$\mu - 2\sigma = 5 - 2(1.5) = 2$$

Question 4

A researcher finds that the mean number of errors per page in a manuscript is $$\mu = 3$$ with a standard deviation $$\sigma = 0.5. $$According to the range rule of thumb, which number of errors per page would be considered not significant?

Accepted Answer

$$X = 3.5$$

Question 5

Which of the following statements is TRUE regarding the use of the range rule of thumb?

Accepted Answer

It is a heuristic guideline and does not represent a formal statistical test.

Chapter 5 Study Guide

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