# Tchebyshev's therom

• July 11th 2010, 04:03 PM
lhotmer
Tchebyshev's therom
The results of a national survey showed that on average, adults sleep 6.9 hours per night.Suppose the standard deviation is 1.2 hours.a. Use the Tchebyshev's therom to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours.b. Use the Tchebyshev's therom to calculate the percentage of individuals who sleep between 3.9 and 9.9 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 4.5 and 9.3 hours per day. How does the result compare to the value that you obtained using Tchebyshev;s theorom in part (a)?
• July 12th 2010, 03:51 AM
pickslides
Quote:

Originally Posted by lhotmer
Use the Tchebyshev's therom to calculate the percentage of individuals who sleep [SIZE=3][FONT=Arial] between 4.5 and 9.3 hours

How many standard deviations from the mean are these bounds?

For $k$ standard deviations then find $1 - \frac{1}{k^2}$