Question

The temperature at any random location in a kiln used in the mansfacture of bricks is normally distributed with a mean of 975 and a standard. deviation of 50 degrees.

If bricks are fired at a temperature above 1095, they wil crack and mutt bo disposed of. If the bricks are placed randamly throughout the hiln, the proportion of bricks that crack during the firing process is closest to __________
(Note: Please enter your answer in docimal form. For example, 5.02% should be entered as 0.0502 )

Answer 1

The proportion of bricks that will crack is found by calculating the z-score for the cracking temperature and then using the standard normal distribution table. The proportion of bricks that will crack is approximately 0.0082 (0.82%).

Step-by-step explanation:

The proportion of bricks that will crack during the firing process in a kiln with a mean temperature of 975 degrees and standard deviation of 50 degrees, when the cracking temperature is above 1095 degrees, can be found using the concept of normal distribution in statistics. To do this, we calculate the z-score for the temperature at which the bricks will crack, which gives us the following:

Z = (X - μ) / σ

Where X is the cracking temperature (1095), μ is the mean temperature (975), and σ is the standard deviation (50).

Substituting the values we get:

Z = (1095 - 975) / 50

Z = 120 / 50

Z = 2.4

Next, we look up the cumulative probability for Z = 2.4 in the standard normal distribution table. This gives us the proportion of the area under the curve to the left of Z. To find the proportion of bricks that will crack, we subtract this value from 1, as we are interested in the right tail (temperatures above the cracking temperature).

For Z = 2.4, the cumulative probability is approximately 0.9918. Thus, the proportion of bricks that crack is about:

1 - 0.9918 = 0.0082

Therefore, the proportion of bricks that will crack during the firing process is approximately 0.0082, or 0.82% when expressed as a decimal.