Quality control engineers create acceptable boundaries for variability within the processes they monitor.They determine that the acceptable boundary for a certain heat exchange process at a gasoline refinery must be set such that under normal operating conditions the threshold would be exceeded only 1% of the time.Under normal operating conditions, the process varies according to a normal distribution, with mean temperature of 231°C and standard deviation of 2.5°C.What upper temperature should they set so that the process will normally exceed the temperature 0.51% of the time?
A) 257.00°C
B) 237.68°C
C) 224.58°C
D) 237.43°C

Question

Quizplus · Accepted Answer

Given that the process should exceed the temperature 0.51% of the time, we look for the z-score corresponding to the upper tail probability of 0.51% (or 0.0051 in decimal form) in the standard normal distribution. This z-score is approximately 2.67. Using the z-score formula $z = \frac{X - \mu}{\sigma}$, where $X$ is the value we're solving for, $\mu = 231°C$ is the mean, and $\sigma = 2.5°C$ is the standard deviation, we can solve for $X$. Rearranging the formula gives $X = \mu + z\sigma = 231 + 2.67(2.5) = 231 + 6.675 = 237.675°C$, which rounds to 237.68°C, making option B the correct answer.

Quality Control Engineers Create Acceptable Boundaries for Variability Within the Processes