SOLUTION: The results of a national survey showed that on average, adults sleep 6.6 hours per night. Suppose the standard deviation is 1.4 hours. a. Use the Tchebyshe

Question 1052583: The results of a national survey showed that on average, adults sleep 6.6 hours per night. Suppose the standard deviation is 1.4 hours.

a. Use the Tchebyshev's theorem to calculate the percentage of individuals who sleep between 3.8 and 9.4 hours.
c. Assume that the number of hours of sleep follows a bell-shaped distributions. Use the
empirical rule to calculate the percentage of individuals who sleep between 3.8 and 9.4 hours per day. How does the result compare to the value that you obtained using Tchebyshev's theorem in part (a)?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
at least 1−1/k2 of the data lie within k standard deviations of the mean
3.8 is 2 standard deviations below the mean
9.4 is 2 standard deviations above the mean
that means 1-1/4 or at least 3/4 of the observations lie between 3.8 and 9.4 hours or a minimum of 75% of individuals sleep between 3.8 and 9.4 hours.
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Empirical rule would say that 97.72% of all observations, a much larger percentage, lie in this interval. Chebyshev's rule is the most conservative; the empirical rule for a normal distribution contains everything that Chebyshev's rule had and more.
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