Binomial Distribution - Admission/Application Essay Example

Binomial distribution: Quality control Binomial distribution: Quality control Question: As a quality engineer working on the Rangdo production line, you have determined that the probability of producing a defective part is 6%. You want to develop a plan to monitor the quality of this line. Your idea is to take a sample of 20 parts every hour and determine the number of defectives. How many defectives do you need to find (or more) in a sample of 20 so that you will shut down the line. You want to be 95% sure that there is a real problem beyond random noise before you shut down the line.

****Use Excel’s binomial function to determine the answer. Provide a one page paper discussing the problem, what you did to solve it and what your specific recommendation or plan is for monitoring quality.SolutionProbability of getting a defective part is 6/100 = 0.06.Number of samples (n) = 20.Confidence interval is 95%. Z 1- α/2 = 1.96 for 95% confidence.DiscussionThe first step is to determine the probability distribution of the 20 samples using excel.The probability distribution for 20 samples XP(X)Defective10.370348720.224573430.086007240.023332050.004766060.00076079.71E-05081.01E-05098.

57E-070106.02E-080113.49E-090121.67E-100136.57E-120142.1E-130155.35E-150161.07E-160171.6E-180181.71E-200191.15E-220203.66E-250The second step is to calculate the 95% confidence interval rangeUsing the above equation, the 95% confidence level will be0.06 ± 1.96 √ (=0.06 ± 0.104=- 0.044 to 0.164Third stepDetermine which values lie outside the range.From the table only two values lie outside this range which means 98% lie within the range. ConclusionThe production should not be stopped because 98% of the products lie within the recommended standards