## Related questions with answers

In 1905, R. Pearl published the article "Biometrical Studies on Man. I. Variation and Correlation in Brain Weight" (Biometrika, Vol. 4, pp. 13-104). According to the study, brain weights of Swedish men are normally distributed with mean 1.40 kg and standard deviation 0.11 kg. Apply the empirical rule to fill in the blanks.

a. Approximately 68 % of Swedish men have brain weights between and

b. Approximately 95 % of Swedish men have brain weights between __ and

c. Approximately 99.7 % of Swedish men have brain weights between and

d. Draw graphs to portray your results.

Solution

VerifiedGiven:

$\mu=1.40$

$\sigma=0.11$

$\textbf{Empirical rule}$ (for roughly bell-shaped distributions)

Approximately 68% of the observations are within 1 standard deviation of the mean.

Approximately 95% of the observations are within 2 standard deviations of the mean.

Approximately 99.7% of the observations are within 3 standard deviations of the mean.

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