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

About 2.28% of the glazed bricks will discolor in the kiln, calculated by finding the z-score for the discoloration temperature of 900°F and using the standard normal distribution.

Step-by-step explanation:

To determine the percentage of glazed bricks that will discolor, we can use the properties of the normal distribution. Given that the mean temperature in the kiln is 1000°F with a standard deviation of 50°F, we must first calculate the z-score for the temperature that causes discoloration, which is 900°F.

To calculate the z-score, use the following formula:

Z = (X - μ) / σ

Where:

• X is the temperature of interest (900°F)
• μ is the mean temperature (1000°F)
• σ is the standard deviation of the temperature (50°F)

Plugging in our values, we get:

Z = (900 - 1000) / 50 = -2

A Z-score of -2 corresponds to the left tail of the normal distribution curve. Using standard normal distribution tables or a calculator, we find that the area to the left of a Z-score of -2 is approximately 2.28%. Therefore, about 2.28% of the glazed bricks will discolor due to the temperature being below 900°F.

Answer 2

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<900)`

Using the z score formula, we have:

`z=(x-\mu)/(\sigma)`

`=(900-1000)/(50)`

`=(-100)/(50)=-2`

Now we have to find
`P(z<-2)`

Using the standard normal table, we have:

`P(z<-2) = 0.0228`

`=2.28\%`

Therefore, 2.28% of glazed bricks will discolor.