A company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Due to many causes- vibration, temperature, wear and tear and the like-the length of the pins...

A company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Due to many causes- vibration, temperature, wear and tear and the like-the length of the pins made by the machines are normally distributed with a mean of 1.008 inches and a standard deviation of 0.045 inch. The company supplies the pins in large batches to a customer. The customer will take a random sample of 50 pins from the batch and compute the sample mean. If the sample mean is within the interval 1.000 inch then the customer will buy the whole batch.Samp