Shafts manufactured for use in optical storage devices have diameters that are normally distributed withmean 0.652 cm and standard deviation 0.003 cm. 30 shafts are selected at random from a large lot and measured, and then the sample standard deviation is computed. The specification for the shaft diameter is 0.650 0.004 cm. If the sample standard deviation
Shafts manufactured for use in optical storage devices have diameters that are
withmean 0.652 cm and standard deviation 0.003 cm. 30 shafts are selected at random
from a large lot and measured, and then the sample standard deviation is computed. The
specification for the shaft diameter is 0.650 0.004 cm. If the sample standard deviation
exceeds 0.004 cm the manufacturing process is reviewed. What is the probability of observing
a sample standard deviation greater than 0.004 cm even though the true standard deviation
is 0.003 cm? In other words, what is the probability that we are ‘unlucky’ enough to only
select enough ‘unacceptable’ shafts (and, therefore, conclude there is something wrong with
the manufacturing process) when, in fact, the actual standard deviation is acceptable and the
process does not need to be reviewed?
Step by step
Solved in 2 steps with 1 images
