The results of a national survey showed that on average adul

The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.2 hours. Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours. At least 93.75 % Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours. At least 96 % Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours per day. 93.75 %

Solution

Z=4.5-6.9/1.2 and 9.3-6.9/1.2=2

z=2

1-1/2^2=3/4 =0.75

so atleast 75%.

Z=3.9-6.9/1.2 and 9.9-6.9/1.2=2.5

1-1/2.5^2=0.84

So atleast 84%

using normdist fucntion in excel for both the values and subtracting them we get 0.9545. So 95.45%.