Respuesta :
Answer:
The answer is "[tex]\bold{Brand \ A \ (35, 350, 18.7) \ \ Brand \ B \ (35, 50, 7.07)}[/tex]"
Explanation:
Calculating the mean for brand A:
[tex]\to \bar{X_{A}}=\frac{10+60+50+30+40+20}{6} =\frac{210}{6}=35[/tex]
Calculating the Variance for brand A:
[tex]\sigma_{A}^{2}=\frac{\left ( 10-35 \right )^{2}+\left ( 60-35 \right )^{2}+\left ( 50-35 \right )^{2}+\left ( 30-35 \right )^{2}+\left ( 40-35 \right )^{2}+\left ( 20-35 \right )^{2}}{5} \\\\[/tex]
[tex]=\frac{\left ( -25 \right )^{2}+\left ( 25 \right )^{2}+\left ( 15\right )^{2}+\left ( -5 \right )^{2}+\left ( 5 \right )^{2}+\left ( 15 \right )^{2}}{5} \\\\ =\frac{625+ 625+225+25+25+225}{5} \\\\ =\frac{1750}{50}\\\\=350[/tex]
Calculating the Standard deviation:
[tex]\sigma _{A}=\sqrt{\sigma _{A}^{2}}=18.7[/tex]
Calculating the Mean for brand B:
[tex]\bar{X_{B}}=\frac{35+45+30+35+40+25}{6}=\frac{210}{6}=35[/tex]
Calculating the Variance for brand B:
[tex]\sigma_{B} ^{2}=\frac{\left ( 35-35 \right )^{2}+\left ( 45-35 \right )^{2}+\left ( 30-35 \right )^{2}+\left ( 35-35 \right )^{2}+\left ( 40-35 \right )^{2}+\left ( 25-35 \right )^{2}}{5}[/tex]
[tex]=\frac{\left ( 0 \right )^{2}+\left ( 10 \right )^{2}+\left ( -5 \right )^{2}+\left (0 \right )^{2}+\left ( 5 \right )^{2}+\left ( -10 \right )^{2}}{5}\\\\=\frac{0+100+25+0+25+100}{5}\\\\=\frac{100+25+25+100}{5}\\\\=\frac{250}{5}\\\\=50[/tex]
Calculating the Standard deviation:
[tex]\sigma _{B}=\sqrt{\sigma _{B}^{2}}=7.07[/tex]
