When a manufacturing process is working properly, cans of tomato juice will contain, on average, 6 ounces of tomato juice. The standard deviation of fill is always .06 ounces. It is known that the fill per can is normally distributed. To monitor the process, a random sample of fifty cans is obtained, the contents are measured, and the sample mean fill is calculated. If the sample mean has a value smaller than 5.975 ounces or larger than 6.025 ounces, the process is deemed to be working improperly and is shut down for repairs.\ Give a complete description (mean, standard error, and shape) of the sampling distribution of (Y ), the sample mean fill of the tomato juice cans when the process is working properly.\ If the process is working properly, what is the probability that a sample of fifty cans would produce a mean that causes the process to be shut down? Halting the process when it is actually working properly is a mistake! Would this mistake happen very often? Explain.\ If the cans are being under-filled by a small amount, say with an average of 5.99 ounces, what is the probability that a sample of fifty cans would produce a mean that detects this problem and causes the process to be shut down? Discuss this probability. \ If the cans are being overfilled by quite a bit, say with an average of 6.05 ounces, what is the probability that a sample of fifty cans would produce a mean that detects this problem and causes the process to be shut down? Discuss this probability.