In the Manufacture of Vitamin Capsules, the Proportion of Calcium

question 54

Essay

In the manufacture of vitamin capsules, the proportion of calcium in each capsule has a specification of parts per million (ppm). A random sample of 100 capsules revealed a sample average calcium content of 44.5 ppm and a sample standard deviation of 3.2 ppm. Management uses and R-charts to monitor the calcium amount using samples of size 4. The charts depict an in-control process.
The centerline of the R chart is 6.7 and the centerline of the chart is 44.8.

a Compute for this process using estimates of the process mean and standard
deviation derived from the random sample.

b. Compute for this process using estimates of the process mean and standard
deviation derived from the control chart parameters.

c. Compute for this process using estimates of the process mean and standard
deviation derived from the random sample.

. Compute for this process using estimates of the process mean and standard
deviation derived from the control chart parameters

d. What do the differences between the values of and tell you?

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Definitions:

Continental Collision

The process whereby two continental plates collide, leading to mountain building and seismic activity.

Subduction

The process by which one tectonic plate moves beneath another plate and sinks into the mantle due to gravitational forces.

Conduction

The process by which heat or electricity is directly transmitted through a substance when there is a difference of temperature or electrical potential.

Subduction Zone

A region where one tectonic plate moves under another, leading to volcanic activity and earthquakes.