{"id":2077,"date":"2024-06-14T17:54:52","date_gmt":"2024-06-14T21:54:52","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&p=2077"},"modified":"2024-06-16T17:45:31","modified_gmt":"2024-06-16T21:45:31","slug":"2077","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/2077\/","title":{"raw":"An Applied Example","rendered":"An Applied Example"},"content":{"raw":"
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Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nApply NORM.DIST and NORM.INV to solve an industry quality control problem.\r\n\r\n<\/div>\r\n<\/div>\r\nIn this section, we will explore a quality control example. For this quality control example, we will examine if the process is producing parts with enough consistency in the production.\r\n

Example 41.1<\/h2>\r\nProblem Setup<\/strong><\/span>: You are purchasing a large batch of 20 centimeter (cm) nuts for your company from a manufacturer.\r\n\r\n[caption id=\"attachment_2117\" align=\"alignnone\" width=\"323\"]\"image<\/a> Figure 41.1 Bolts produced by manufacturer.[\/caption]\r\n\r\nBefore paying for the nuts \u2013 you perform quality control on the batch because you need these nuts to fit onto certain bolts in the product you are making.\r\n\r\n[caption id=\"attachment_2122\" align=\"alignnone\" width=\"323\"]\"Image<\/a> Figure 41.2 Nuts with 20 cm bolts affixed to them.[\/caption]\r\n\r\nSampling<\/strong><\/span>: You take a sample of nuts and measure the diameter of each. In order to pass quality control, the sample can only have 5% of nuts smaller than 19.8 cm in diameter. Note: We will talk a lot more about sampling in the next section!\r\n\r\nResults<\/strong><\/span>: In the sample of nuts that you gather, you find that the average diameter is 20.1cm with a standard deviation of 0.1cm.\r\n\r\nQuestion<\/strong><\/span>: Will you accept this batch from the manufacturer?\r\n

Method #1 to Solve Problem (Exercise)<\/h1>\r\nYou Try: <\/strong><\/span>Let us first calculate the diameter that 5% of the nuts in our sample are smaller than. In order to do this, let us first choose the correct diagram we will use to solve this problem:\r\n
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[h5p id=\"141\"]<\/div>\r\n<\/div>\r\nNext, let us pick the correct Excel command to solve for the [latex]x[\/latex]-value in question:\r\n
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[h5p id=\"142\"]<\/div>\r\n<\/div>\r\nFinally, let's draw a conclusion based off of our results:\r\n
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[h5p id=\"143\"]<\/div>\r\n<\/div>\r\nHelp to solve this problem?<\/strong><\/span> Click here<\/a> for the Powerpoint slides. Click here<\/a> for the Excel solutions. See below for the video solution and click below to reveal the written solutions.\r\n
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Click here to reveal the written solutions for Method # 1<\/h1>\r\n1)<\/span><\/strong> Let us first calculate the diameter that 5% of the nuts in our sample are smaller than. In order to do this, let us first choose the correct diagram we will use to solve this problem:\r\n\r\n[caption id=\"attachment_2138\" align=\"aligncenter\" width=\"364\"]\"Bell<\/a> Figure 41.3 Left 5% of bell curve highlighted.[\/caption]\r\n\r\n2)<\/strong> <\/span>Second, let us determine the Excel formula to calculate the [latex]x[\/latex]-value from the above diagram: \\[ x = \\text{NORM.INV}(0.05, 20.1, 0.1) = 19.93551 \\]\r\n\r\n3)<\/strong> <\/span>Finally, we can conclude that, because 19.93551cm is larger than the required 19.8cm limit, the nuts are large enough in diameter. Ie: More than 5% of the nuts are larger in diameter than 19.8cms and we can accept the batch of nuts from the manufacturer.\r\n\r\n[caption id=\"attachment_2146\" align=\"aligncenter\" width=\"364\"]\"Bell<\/a> Figure 41.4 5% area is less than 19.94 cms.[\/caption]\r\n\r\n<\/div>\r\n

Method #2 to Solve Problem (Exercise)<\/h1>\r\nYou Try: <\/strong><\/span>Let us now solve the problem by determining the percent of nuts that have a diameter less than 19.8cm in the sample:\r\n
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[h5p id=\"144\"]<\/div>\r\n<\/div>\r\nNext, let us pick the correct Excel command to solve for the [latex]x[\/latex]-value in question:\r\n
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[h5p id=\"145\"]<\/div>\r\n<\/div>\r\nFinally, let's draw a conclusion based off of our results:\r\n
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[h5p id=\"146\"]<\/div>\r\n<\/div>\r\nHelp to solve this problem?<\/strong><\/span> Click here<\/a> for the Powerpoint slides. Click here<\/a> for the Excel solutions. See below for the video solution and click below to reveal the written solutions.\r\n
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Click here to reveal the written solutions for Method # 2<\/h1>\r\n1)<\/span><\/strong> Let us first calculate the percent of nuts with a diameter less than 19.8 cms. In order to do this, let us first choose the correct diagram we will use to solve this problem:\r\n\r\n[caption id=\"attachment_2149\" align=\"aligncenter\" width=\"360\"]\"Bell<\/a> Figure 41.5 Unknown area below 19.8 cms.[\/caption]\r\n\r\n2)<\/strong> <\/span>Second, let us determine the Excel formula to calculate the unknown area in the above diagram: \\[ area = \\text{NORM.DIST}(19.8, 20.1, 0.1, 1) = 0.00135 \\]\r\n\r\n3)<\/strong> <\/span>Finally, we can conclude that, because 0.00135 = 0.135% is smaller than the limit of 5%, enough of the nuts are larger than the limit of 19.8cms in diameter. Ie: Less than 5% of the nuts are smaller in diameter than 19.8cms and we can accept the batch of nuts from the manufacturer.\r\n\r\n[caption id=\"attachment_2150\" align=\"aligncenter\" width=\"360\"]\"Bell<\/a> Figure 41.6 Areas to the left of 19.94 and 19.8cms.[\/caption]\r\n\r\n<\/div>\r\n

Video Solution to This Section's Example<\/h1>\r\nhttps:\/\/youtu.be\/jwNA5CTrCXg\r\n

Accompanying Resources<\/h2>\r\n