Normal Distribution Review Exercises
Review your Statistics notes concerning the normal probability
distribution. Then work the following problems:
- The pipefitting contractor for some work to be done on the heating,
ventilating, and air conditioning (HVAC) system in the Business
Building has summed her estimates for the various stages of the
project. She has determined that the expected (i.e., average)
time a job like this should take is 55 days, with a
standard deviation of 5 days. In addition, it is
typical for completion times of projects like this to be approximately
normally distributed. The contract specifies that the contractor must
complete the job within 2 months of the starting
date. If the work is not completed within that time frame, the
contractor will be required to pay liquidated damages of $1,000 per
day. Based upon her estimates what is the probability the contractor
will be required to pay at least some liquidated damages?
- Plug-N-Go makes valve covers to a diameter specification of 0.500
plus or minus 0.020 cm. If the normally distributed process
averages 0.510 cm with an estimated standard
deviation of 0.004 cm, what percentage of the output
meets specifications?
- Leadtime demand for the resupply of motor oil at a
local service station has averaged around 800 quarts with a
standard deviation of 120 quarts. Records over the
past several years indicate that demand appears to be normally
distributed. If it is policy to reorder when current on-hand inventory
is sufficient to guarantee a 90% probability that no shortage
will occur, what should the reorder point (ROP) be?
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