Question

A testing lab wishes to test two experimental brans of outdoor pain long each wiil last befor fading . The testing lab makes six gallon s of each paint to test. The resultare Shown to see how

Answer 1

Answer:

The answer is "$\bold{Brand \ A \ (35, 350, 18.7) \ \ Brand \ B \ (35, 50, 7.07)}$"

Explanation:

Calculating the mean for brand A:

$\to \bar{X_{A}}=\frac{10+60+50+30+40+20}{6} =\frac{210}{6}=35$

Calculating the Variance for brand A:

$\sigma_{A}^{2}=\frac{\left ( 10-35 \right )^{2}+\left ( 60-35 \right )^{2}+\left ( 50-35 \right )^{2}+\left ( 30-35 \right )^{2}+\left ( 40-35 \right )^{2}+\left ( 20-35 \right )^{2}}{5}$

     $=\frac{\left ( -25 \right )^{2}+\left ( 25 \right )^{2}+\left ( 15\right )^{2}+\left ( -5 \right )^{2}+\left ( 5 \right )^{2}+\left ( 15 \right )^{2}}{5} \\\\ =\frac{625+ 625+225+25+25+225}{5} \\\\ =\frac{1750}{50}\\\\=350$

Calculating the Standard deviation:

$\sigma _{A}=\sqrt{\sigma _{A}^{2}}=18.7$

Calculating the Mean for brand B:

$\bar{X_{B}}=\frac{35+45+30+35+40+25}{6}=\frac{210}{6}=35$

Calculating the Variance for brand B:

$\sigma_{B} ^{2}=\frac{\left ( 35-35 \right )^{2}+\left ( 45-35 \right )^{2}+\left ( 30-35 \right )^{2}+\left ( 35-35 \right )^{2}+\left ( 40-35 \right )^{2}+\left ( 25-35 \right )^{2}}{5}$

    $=\frac{\left ( 0 \right )^{2}+\left ( 10 \right )^{2}+\left ( -5 \right )^{2}+\left (0 \right )^{2}+\left ( 5 \right )^{2}+\left ( -10 \right )^{2}}{5}\\\\=\frac{0+100+25+0+25+100}{5}\\\\=\frac{100+25+25+100}{5}\\\\=\frac{250}{5}\\\\=50$

 Calculating the Standard deviation:  

$\sigma _{B}=\sqrt{\sigma _{B}^{2}}=7.07$