You and your know-it-all boss are sitting in a meeting reviewing recent data on

Question

You and your know-it-all boss are sitting in a meeting reviewing recent data on product demand at Lopez International Products. A frequency distribution of demand made up of many observations is presented along with the mean and standard deviation of the data. You carefully observe the shape of the frequency distribution looking for a hint of general form--it certainly doesn't appear to be Normal or even Uniform. Finally, your boss says: Well, it is obvious to me that 95% of the data lie within 2 standard deviations above and below the mean. I'll stake my reputation on it! The interpretation of this data is very important to the firm; thus, great caution must be exercised in making statements about the proximity of the data to the mean of the distribution.

Which of the following is true (pick one)?

Explanation / Answer

As per Chebyshev's theorem, (1 - 1/k^2) lies between k standard deviation from the mean.

So,

In 2 standard deviation, (1 - 1/4) i.e. 0.75 or 75% data lies between 2 standard deviation from the mean.

Option B is correct.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.