5. + -/3.75 points ASVVSBE 13 3 E.039.Ml. 0/3 Submissions used My Note The resul

Question

5. + -/3.75 points ASVVSBE 13 3 E.039.Ml. 0/3 Submissions used My Note The results o a national survey showed that on average, adults sleep 6.3 hours per night. Suppose that the standard deviation is 1.2 hours. (a) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.9 and 8.7 hours. (b) Use Chebyshev's theorem to calculate the minimum percentage of individuals who sleep between 3.3 and 9.3 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 3.9 and 8.7 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 isSelectthe percentage obtained using Chebyshev's theorem

Explanation / Answer

a)

from Chebychev ; k std deviaiton away data contain (1-1/k2 ) *100 % values

as 3.9 abd 8.7 are 2 std deviation away ; hence % of value=(1-1/22)*100 =75.0%

b)

as 3.3 and 9.3 are 2.5 std deviation away ; hence % of value=(1-1/2.52)*100 =84.0%

c)

from empiritcal rule 2 std deviation away values =95.0%

d)

the percentage obtained using the emprirical rule is greater than the percentage obtained using Chebychev;s rule

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