# Question: The characteristics of an industrial filling process in which an

The characteristics of an industrial filling process in which an expensive liquid is injected into a container were investigated in the Journal of Quality Technology (July 1999). The quantity injected per container is approximately normally distributed with mean 10 units and standard deviation .2 unit. Each unit of fill costs $20. If a container contains less than 10 units (i.e., is under filled), it must be reprocessed at a cost of $10. A properly filled container sells for $230.

a. Find the probability that a container is underfilled.

b. A container is initially underfilled and must be reprocessed. Upon refilling, it contains 10.6 units. How much profit will the company make on this container?

c. The operations manager adjusts the mean of the filling process upward to 10.5 units in order to make the probability of underfilling approximately zero. Under these conditions, what is the expected profit per container?

a. Find the probability that a container is underfilled.

b. A container is initially underfilled and must be reprocessed. Upon refilling, it contains 10.6 units. How much profit will the company make on this container?

c. The operations manager adjusts the mean of the filling process upward to 10.5 units in order to make the probability of underfilling approximately zero. Under these conditions, what is the expected profit per container?

## Relevant Questions

In the Journal of the International Association for Shell and Spatial Structures (April 2004), Japanese environmental researchers studied the performance of truss-and-frame structures subjected to uncertain loads. The load ...Examine the following sample data saved in the LM5_60 file. a. Construct a stem-and-leaf plot to assess whether the data are from an approximately normal distribution. b. Compute s for the sample data. c. Find the values ...Why do we need a correction for continuity when approximating a binomial probability with the normal distribution? The percentage of fat in the bodies of American men is an approximately normal random variable with mean equal to 15% and standard deviation equal to 2%. a. If these values were used to describe the body fat of men in the ...An essential tool in the monitoring of the quality of a manufactured product is acceptance sampling. An acceptance sampling plan involves knowing the distribution of the life length of the item produced and determining how ...Post your question