Also , show that you ensured that the sum of the probabilities of all possible outcomes is 1. c. 2 points: Again , suppose that Intel Corp .'s shipment contains 10 % defective microprocessors In cell C11 , find the average number of defectives we expect in a sample of 5 microprocessors 4 points: Again , suppose that Intel Corp .'s shipment contains 10% defective microprocessors In cell C13, provide the probability that the entire shipment will be returned (assuming 10% defect rate and 5 microprocessors sampled ). 4 points: In cell C15, calculate the probability that the entire shipment will be kept by Gateway even though the shipment has 10% defective microprocessors assuming 5 microprocessors are sampled Question 3 Asterex Inc. produces silicon gaskets that are used to connect piping materials for the petroleum industry. The gaskets are ring shaped, and look like a thin donut with a big hole in the center. It is important that the gaskets have the proper inside diameter (ID), outside diameter (OD), and wall thickness. The quality control department samples and tests gaskets every 15 minutes to ensure conformance to quality characteristics and engineering specifications for the three quality dimensions Recently, there has been some concern about the OD of the gaskets. A sample of 100 gasket OD measures was taken and the data is in column B. If the gasket production machine is working properly, the population of gasket OD measures can be reasonably modeled by a Normal distribution with mean OD = 400 mm and standard deviation OD = 2 mm . Use the spreadsheet named Asterex 8 points: Find the values for the sample statistics indicated in column D. Use a built-in Excel function or formula when appropriate. Place the appropriate function or formula for each statistics in the indicated cell in column b . 4 points: Notice that the sample mean you calculated in the previous question was just one of many that could have been obtained. That is, many samples of size 100 could have been taken, and each sample would result in a different (but close) sample mean. As a result, the sample means tend to vary around the grand population mean , as do individual values , but the variance sample means is smaller. The standard deviation measures variation of individual data values around the population mean, while the standard error measures variation of sample means around the population mean. In cell E13, write a formula that calculates the standard error (SE ) based on an assumed process mean of 400 mm , standard deviation of 2 mm , and sample of size 100 c. 6 points: The population of possible sample means is assumed normally distributed since the underlying sample values were normally distributed. Since this is the case, we can use the Empirical Rule to determine the lower and upper limit (interval) of expected sample means based on samples of size 100. That is, we can use the interval to predict the range of possible values of sample means when the process is working correctly. Use the Empirical Rule to determine the two values between which we expect to see almost all sample means (of size 100) when the process is working. You must write a formula that references the assumed parameters . When we say almost all, we mean 99.7% of data, which is contained between = 3 SE of the population mean. Write the formula for the lower limit in cell E19, and for the upper limit in F19. See equation 7.2 on page 320 of our text for guidance