One operation of a mill is to cut pieces of steel into parts that will later be used as the frame for front seats in an automobile. The steel is cut with a diamond saw and requires

Question

the resulting parts to be within ±0.005 inch of the length specified by the automobile company. The data in the file
comes from a sample of 100 steel parts. The measurement reported is the difference in inches between the actual
length of the steel part, as measured by a laser measurement device, and the specified length of the steel part. For example, the first value, 0.002, represents a steel part that is 0.002 inch shorter than the specified length.
a. Construct a percentage histogram.
b. Is the steel mill doing a good job in meeting the requirements set by the automobile company? Explain.

Steel File:

Error
-0.002
0.0005
0.0025
0.001
0.002
0.001
0.005
-0.002
0
0.001
-0.0025
-0.003
0.001
-0.0005
0
-0.003
-0.001
0.0005
0.0025
-0.0025
0.002
0.001
0.001
0.001
-0.002
-0.003
-0.0015
-0.0005
0
-0.0025
-0.003
-0.001
0.002
-0.001
0
0.003
0.0015
0
0
-0.0025
0.0005
0.001
0.0005
0.001
0.0025
0.001
0
-0.0025
-0.001
0.0035
0
-0.003
-0.002
-0.001
-0.0015
-0.0015
-0.002
0.001
-0.0025
-0.0005
-0.0015
-0.0005
-0.0015
-0.0005
-0.0005
-0.001
-0.0015
0.0025
0.001
0.0005
0
-0.002
-0.0005
0.0005
0.0005
0
-0.0005
0.002
0.001
-0.0015
-0.001
-0.001
0.0005
-0.0025
0.0025
0.002
0.0025
-0.002
0
-0.0005
-0.001
0
-0.002
0
0
0.002
-0.003
-0.0005
-0.002
-0.002

Answer 1

-0.001
-0.001
0.001
0.001
0.001
0.0005
0.0005
0.001
-0.001
-0.001
-0.0005
-0.001
-0.0005
0.0005
0.001
0.0005
0.0005
0.001
0.0005
0.0005
0.0005

a. A percentage histogram of the data can be constructed by counting the number of values that fall within each range of errors and then converting that count into a percentage of the total number of values. For example, the range of errors from -0.003 to -0.002 includes 4 values, which is 4% of the total number of values.

b. The steel mill is doing a good job in meeting the requirements set by the automobile company. The data shows that the majority of the steel parts are within ±0.005 inch of the specified length, with the majority of the errors being less than 0.002 inch. This indicates that the steel mill is meeting the requirements set by the automobile company.