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Binomial Distribution - Admission/Application Essay Example

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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…
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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.
Solution
Probability 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.
Discussion
The first step is to determine the probability distribution of the 20 samples using excel.
The probability distribution for 20 samples
X
P(X)
Defective
1
0.370348
7
2
0.224573
4
3
0.086007
2
4
0.023332
0
5
0.004766
0
6
0.00076
0
7
9.71E-05
0
8
1.01E-05
0
9
8.57E-07
0
10
6.02E-08
0
11
3.49E-09
0
12
1.67E-10
0
13
6.57E-12
0
14
2.1E-13
0
15
5.35E-15
0
16
1.07E-16
0
17
1.6E-18
0
18
1.71E-20
0
19
1.15E-22
0
20
3.66E-25
0
The second step is to calculate the 95% confidence interval range
Using the above equation, the 95% confidence level will be
0.06 ± 1.96 √ (
=0.06 ± 0.104
=- 0.044 to 0.164
Third step
Determine which values lie outside the range.
From the table only two values lie outside this range which means 98% lie within the range.
Conclusion
The production should not be stopped because 98% of the products lie within the recommended standards Read More
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