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The results of a national survey showed that on average, adults sleep hours per night. Suppose that the standard deviation is hours. Round your answers to the nearest whole number. a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between and hours. At least b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between and hours. At least 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 and hours per day. At least

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Answer:

Following are the solution to the given question:

Step-by-step explanation:

For point a:

[tex]6.5 - 4.9 = 2.4 \\\\\frac{2.4}{1.2} = 2 \\\\\sigma \ \ so \ k = 2[/tex]

For point b:

[tex]\frac{3}{1.2}\ \ \sigma\ \ so \ k =\frac{3}{1.2} \ \ so\ \ 1- \frac{1}{k ^2} = 0.84[/tex]

For point c:

Once again, we have k = 2 though with Chebyshev discrepancy of witness numbers in the same number of standard deviations off mean = at least 75 percent.

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