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(4) Suppose you are a quality manager in a company that produces portable electric heaters. The quality of the heater is measured by the temperature

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(4) Suppose you are a quality manager in a company that produces portable electric heaters. The quality of the heater is measured by the temperature of the air at 4 feet away from the heater when the heater is set at its maximum setting, 80 F degrees. Your customers would not appreciate if the heater fails to heat enough or if it heats too much. Accordingly, product designers set the lower and upper tolerance limits at 75 F and 85 F degrees, respectively. You are randomly picked a sample of 20 products and record the following temperatures. 80.5 74.8 83.9 80.2 80 82.6 77.8 82.4 80.2 77.6 82.9 80.6 80.7 79.2 81.5 83.4 80.3 74.5 75.4 81.5 a) What is the average temperature (X-bar)? (the correct answer is an integer) b) What is the sample standard deviation (c)? (Use STDEV.S formula in Excel, keep at least 3 decimals, example of a correct format; 1.342) c) What is the sigma capability measure (z)? (keep at least 3 decimals, example of a correct format; 1.342) d) What is the probability of meeting the specifications? Use the NORMSDIST formula in Excel (keep at least 4 decimals, example of a correct format; 0.9102) (4) Suppose you are a quality manager in a company that produces portable electric heaters. The quality of the heater is measured by the temperature of the air at 4 feet away from the heater when the heater is set at its maximum setting, 80 F degrees. Your customers would not appreciate if the heater fails to heat enough or if it heats too much. Accordingly, product designers set the lower and upper tolerance limits at 75 F and 85 F degrees, respectively. You are randomly picked a sample of 20 products and record the following temperatures. 80.5 74.8 83.9 80.2 80 82.6 77.8 82.4 80.2 77.6 82.9 80.6 80.7 79.2 81.5 83.4 80.3 74.5 75.4 81.5 a) What is the average temperature (X-bar)? (the correct answer is an integer) b) What is the sample standard deviation (c)? (Use STDEV.S formula in Excel, keep at least 3 decimals, example of a correct format; 1.342) c) What is the sigma capability measure (z)? (keep at least 3 decimals, example of a correct format; 1.342) d) What is the probability of meeting the specifications? Use the NORMSDIST formula in Excel (keep at least 4 decimals, example of a correct format; 0.9102)

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