Acceptable Pins

Read the Case – Acceptance Sampling of Pins of Complete Business Statistics and answer the following questions. Also use the templates to verify the answer. Check and see the effect on acceptance of pins, when the mean and standard deviations are manipulated. Identify the most profitable situation based on cost of reengineering. 1. What is the probability that a batch will be acceptable to the consumer and if the probability is large enough to be an acceptable level of performance?If the population mean and standard deviation of the length of the pins are adjusted in order to improve the percentage accepted, which one do you think in practice is easier to adjust, the mean or the SD and why? 3. If the lathe can be adjusted to have the mean of the lengths to any desired value, what should it be adjusted to and why? 4. If the mean cannot be adjusted, but the SD can be reduced, what maximum value of the SD would make 90%, 95% and 99% of the parts acceptable to the consumer? (Assum e the mean to be 1. 008 inches).5. Considering the cost of resetting the machines (to adjust the population mean involving the engineer’s time, re-engineering process and cost of production time lost): 1. Assume it costs $150 x2 to decrease the SD by (x/1000) inch. Find the cost of reducing the SDs to the values found in question no. 4. 2. Assume that the mean has been adjusted to the best value at a cost of 80$, calculate the SD necessary to have 90%, 95% and 99% of the parts acceptable and their costs. 3. Based on the above, what is your recommended mean and SD? Verify your answers by using excel templates.Format your report consistent with APA guidelines. CASE Acceptance Sampling of Pins A company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Factors such as vibrations, temperature, wear and tear affect the pins, so that the lengths of the pins made by the machine are normally distributed with a mean of 1. 008 inches and a st andard 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  ± 0. 010 inch, then the customer will buy the whole batch. To improve the probability of acceptance, the production manager and the engineers discuss adjusting the population mean and Standard deviation of the length of the pins. The production manager then considers the costs involved. The cost of resetting the machine to adjust the population mean involves the engineers’ time and the cost of production time lost. The cost of reducing the population standard deviation involves, in addition to these costs, the cost of overhauling the machine and reengineering the process.