Question

The temperature at any random location in a kiln used for manufacturing bricks is normally distributed with a mean of 1000°f and a standard deviation of 50°f. when glazed bricks are put in the oven, if the temperature is below 900°f, they will discolor. if the bricks are placed randomly throughout the kiln, what percentage of glazed bricks will discolor?

Answer 1

Solution: We are given:

Temperature at any random location in a kiln used for manufacturing bricks is normally distributed with mean $\mu=1000,$ standard deviation $\sigma =50$

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 $P(x$

Using the z score formula, we have:

$z=\frac{x-\mu}{\sigma}$

        $=\frac{900-1000}{50}$

        $=\frac{-100}{50}=-2$

Now we have to find $P(z$

Using the standard normal table, we have:

$P(z$

                  $=2.28\%$

Therefore, 2.28% of glazed bricks will discolor.