Q6. The operations manager at a brewery that runs 24 hours per day has determined that...

 

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Q6. The operations manager at a brewery that runs 24 hours per day has determined that the amount of production time lost each day (24-hour period) due to equipment failure is a normally distributed random variable, X. Historically, the population mean amount of lost time has been assumed to be u = 3.4 hours per day. The manager decides to upgrade the equipment and after 4 months, he will select another random sample of 36 days and compute the average amount of lost time. In order to justify the purchase of the new equipment, he is now looking for sufficient evidence to conclude that the population mean amount of lost time is less than 3.4 hours per day. As such, the hypotheses are Ho: 23.4 hours and H. <3.4 hours, and he chooses to use a level of significance of a = 0.025. If it is true that the population mean amount of lost time is now = 2.21 hours per day and the standard deviation of the lost time is σ = 1.5 hours, what is the probability that the manager will conclude that the population mean amount of lost time is less than 3.4 hours? (Note: This is the correct conclusion to reach under these conditions.) A. 0.9750 B. 0.0026 C. 0.7704 D. 0.0250 E. 0.9974 Q6. The operations manager at a brewery that runs 24 hours per day has determined that the amount of production time lost each day (24-hour period) due to equipment failure is a normally distributed random variable, X. Historically, the population mean amount of lost time has been assumed to be u = 3.4 hours per day. The manager decides to upgrade the equipment and after 4 months, he will select another random sample of 36 days and compute the average amount of lost time. In order to justify the purchase of the new equipment, he is now looking for sufficient evidence to conclude that the population mean amount of lost time is less than 3.4 hours per day. As such, the hypotheses are Ho: 23.4 hours and H. <3.4 hours, and he chooses to use a level of significance of a = 0.025. If it is true that the population mean amount of lost time is now = 2.21 hours per day and the standard deviation of the lost time is σ = 1.5 hours, what is the probability that the manager will conclude that the population mean amount of lost time is less than 3.4 hours? (Note: This is the correct conclusion to reach under these conditions.) A. 0.9750 B. 0.0026 C. 0.7704 D. 0.0250 E. 0.9974

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