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

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

Step-by-step explanation:

Calculating the mean for brand A:

`\to \bar{X_(A)}=(10+60+50+30+40+20)/(6) =(210)/(6)=35`

Calculating the Variance for brand A:

`\sigma_(A)^(2)=(\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) \\\\`

`=(\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) \\\\ =(625+ 625+225+25+25+225)/(5) \\\\ =(1750)/(50)\\\\=350`

Calculating the Standard deviation:

`\sigma _(A)=\sqrt{\sigma _(A)^(2)}=18.7`

Calculating the Mean for brand B:

`\bar{X_(B)}=(35+45+30+35+40+25)/(6)=(210)/(6)=35`

Calculating the Variance for brand B:

`\sigma_(B) ^(2)=(\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)`

`=(\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)\\\\=(0+100+25+0+25+100)/(5)\\\\=(100+25+25+100)/(5)\\\\=(250)/(5)\\\\=50`

Calculating the Standard deviation:

`\sigma _(B)=\sqrt{\sigma _(B)^(2)}=7.07`