Solution: We are given:
Temperature at any random location in a kiln used for manufacturing bricks is normally distributed with mean [tex]\mu=1000,[/tex] standard deviation [tex]\sigma =50[/tex]
We have to find the percentage of glazed bricks that will discolor. A brick will discolor if the temperature is below 900°f.
Therefore, we have to find [tex]P(x<900)[/tex]
Using the z score formula, we have:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]=\frac{900-1000}{50}[/tex]
[tex]=\frac{-100}{50}=-2[/tex]
Now we have to find [tex]P(z<-2)[/tex]
Using the standard normal table, we have:
[tex]P(z<-2) = 0.0228[/tex]
[tex]=2.28\%[/tex]
Therefore, 2.28% of glazed bricks will discolor.
