Answer Happy

In statistics, when we describe a distribution, we give the shape (if known), the center, and the spread. Usually the center is the mean and the spread is the standard deviation. Example. As part of a manufacturing process, a certain machine drills holes in metal with a mean width of 0.750 inches and a standard deviation of 0.020 inches. The width of these holes form a distribution that is known to be normal. Each day, a random sample of 20 holes is measured and checked to ensure the machine remains set to the correct tolerance. Using complete sentences and an essay format, describe the sampling distribution of the sample mean. Answer. The sampling distribution of the sample mean for samples of size 20 taken from the population with mean 0.750 inches and standard deviation 0.020 inches is mound- shaped and symmetrical, or normal in shape, even though the sample size is not large, because the population distribution from which the samples are taken is known to be normal. The mean of the sampling distribution is 0.750 inches and the standard deviation is 0.020 = 0.004472135955, or about 0.0045 inches. 20 Practice. The daily revenues for a food truck form a distribution that is skewed left, because while the revenue is usually consistent, when it rains the daily revenue is much less. The owner of the food truck has calculated over a lengthy period that the average daily revenue is $1200 with a standard deviation of $225. If the owner observes a random sample of 50 days from the past five years of operation, describe the sampling distribution of the sample mean for the daily revenue.