1. A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected...

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Question:

1. A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain no more than 2 rejects?

B. At least 2 rejects?

2. The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 7. Find the probability that more than four road construction projects are currently taking place in the city.

3. The target value for the thickness of a machined cylinder is 8cm. The upper specification limit is 8.2cm and the lower specification limit is 7.9cm. A machine produces cylinders that have a mean thickness of 8.1cm an d a standard deviation of 0.1cm.

A. What is the probability that the thickness of a randomly selected cylinder is within specification?

B. What is the probability that the thickness of a randomly selected cylinder exceeds the target value?

? What is the probability that the thickness of a randomly selected cylinder is less than the lower specification limit?

4. The average life of a certain type of motor is 10 years, with a standard deviation of 2 years. If the manufacturer is willing to replace only 3% of the motors that fail, how long a guarantee should he offer? Assume that the lives of the motors follow a Normal distribution.

5. Sam�s Long Life 75-watt light bulbs are designed to have a life of 1125 hours with tolerances of � 210 hours. The process that makes light bulbs has a mean of 1050 hours, with a standard deviation of 55 hours. Determine the proportion of parts outside the specifications. Assume Normal Distribution.

6. Elon Corporation manufactures parts for an aircraft company. It uses a computerized numerical controlled (CNC) machining center to produce a specific part that has a design (nominal) target of 1.275 inches with tolerances of �.024 inch. The CNC process that manufacturers these parts has a mean of 1.281 inches and a standard deviation of 0.008 inch. Determine the proportion of parts outside the specifications.

Assume Normal Distribution.