Question

guided practice activity #12 - the black swan by nassim taleb
why does he call the normal distribution the great intellectual fraud?
because socio - economic data is usually not normal but economists models all use the normal distribution!
example: us household income 2005
\\( \mu=\\$ 84,800 \\) and \\( \sigma=\\$ 386,000 \\) note: median value \\( =\\$ 58,500 \\)

1. what does the mean being greater than the median tell you about the data set?
2. the top \\( 0.01 \\% \\) of households averaged \\( \\$ 35,473,200 \\). compute the corresponding \\( z \\)-score (1 decimal place).
3. u.s. women 20 years and older have an average height of 63.7 inches with a standard deviation of 2.8 inches. how tall would a woman be if she had the same \\( z \\)-score computed in #2 above (1 decimal place)?
4. what is a \black swan\ a metaphor for in economic terms?

Explanation:

Step1: Recall the property of skewness

In a data - set, if the mean \(\mu\) is greater than the median \(M\), the data is skewed to the right. This is because the mean is influenced by large values (outliers) in the right - tail of the distribution.

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\). Given \(x = 35473200\), \(\mu=84800\), and \(\sigma = 386000\).

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Step3: Use the z - score formula for height

We know \(z\approx91.7\), \(\mu = 63.7\) (height mean) and \(\sigma=2.8\) (height standard deviation). Using the formula \(x=\mu+z\sigma\)

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Step4: Define the black - swan metaphor

In economic terms, a “black swan” is a metaphor for an extremely rare, unpredictable event with severe consequences. These events are often rationalized after they occur but are difficult to predict using traditional economic models.

Answer:

1. The data set is skewed to the right.
2. \(z\approx91.7\)
3. \(x = 320.5\) inches
4. An extremely rare, unpredictable event with severe consequences.