The results of a national suvey showed that on average, aours seep (a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sieep between 37 and 93 hours (b) Use Chebyshev's theorem to calculate the minimum percentage of individuals whe sleep between 3 and 10 heurs () Assume thhat the number of hours of sieep folows a bel shaped distribution. Use the empirical rule to calculate the percentage of individuals whe sieep between 37and93 hours per day How does this result compare to the value that you obtained using Chebyshev's theorem in part (a) The percentage obtained using the empirical rule isSelect the percentage obtained using Chebyshev's theorem

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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The text from the image on the educational website reads:

"The results of a national survey showed that on average, adults sleep 6.8 hours per night. Suppose that the standard deviation is 1.4 hours.

(a) Use Chebyshev’s theorem to calculate the minimum percentage of individuals who sleep between 3.7 and 9.9 hours.

(b) Use Chebyshev’s theorem to calculate the minimum percentage of individuals who sleep between 1 and 10 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 3.7 and 9.9 hours per day.

How does this result compare to the value that you obtained using Chebyshev’s theorem in part (a)?

The percentage obtained using the empirical rule is [Select] the percentage obtained using Chebyshev’s theorem."

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Transcribed Image Text:The text from the image on the educational website reads: "The results of a national survey showed that on average, adults sleep 6.8 hours per night. Suppose that the standard deviation is 1.4 hours. (a) Use Chebyshev’s theorem to calculate the minimum percentage of individuals who sleep between 3.7 and 9.9 hours. (b) Use Chebyshev’s theorem to calculate the minimum percentage of individuals who sleep between 1 and 10 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 3.7 and 9.9 hours per day. How does this result compare to the value that you obtained using Chebyshev’s theorem in part (a)? The percentage obtained using the empirical rule is [Select] the percentage obtained using Chebyshev’s theorem." Below the text, there are navigation buttons labeled "Need Help?", "Read It", "Watch It", and "Master It".
Expert Solution
Step 1

a)

Consider that a random variable X has expected value μ and standard deviation, σ. Now, according to Chebyshev’s Inequality, it can be said that:

P(| Xμ | < ) ≥ 1 – (1/k2), where k is any positive real number.

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