Answer: a) 25%
b) 75% Chebyshev interval around the sample mean=(6,18)
Step-by-step explanation:
Given: Sample mean: [tex]\overline{x}=12[/tex]
Sample standard deviation: s= 3
a) Coefficient of variation = [tex]\dfrac{s}{\overline{x}}\times100[/tex]
[tex]\\\\=\dfrac{3}{12}\times100\%=\dfrac{100\%}{4}\\\\=25\%[/tex]
b) According to the Chebychev's theorem,
75% of the population lies within 2 standard deviations from the sample mean.
i.e. 75% Chebyshev interval around the sample mean. = [tex](\overline{x}-2s,\ \overline{x}+2s)[/tex]
[tex]=(12-2(3),\ 12+2(3))\\\\=(6, 18)[/tex]
Hence, the 75% Chebyshev interval around the sample mean=(6,18)
