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. a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours. b. Use Chebyshev's theorem 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 distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours per day. How does this result compare to the value that you obtained using Chebyshev's theorem in part (a) ?

Answer:a) 75% b) 84% c) 95%

Empirical rule states that the data shows approximately 68% of data within 1 standard deviation.

Approximately 95% data is within 2 standard.

Approximately 99.7% of data is within 3 standard deviation

The interval in hrs per night of 4.5 - 9.3 is within 2 standard deviation which means that there is approximately 95% of the data within 2 standard deviation.

95% of adults sleep on average from 4.5 - 9.3 hours per night.

At least 75% of adults sleep on average 4.5-9.3 hrs per night

Step-by-step explanation:Chebshev Theorem is given by:

(1 - (1/z^2)) * 100 ... equation (1)

a) Interval 4.5 to 9.3 hours per night

Difference = 9.3-4.5=4.8

Mean = 4.8/2 = 2.4

Z = 2.4/1.2 = 2

Substituting into eq 1

(1 - (1/2^2)) * 100

(4-1/4) * 100

=75%

b) Interval 3.9 to 9.7 hours per night

Difference = 9.7 - 3.9 = 6

Mean = 6/2 = 3

Z = 3/1.2 = 2.5

Substituting into equation (1)

(1 - (1/2.5^2)

(1 - (1/6.25)

= 84%