The distribution of actual weights of wedges of cheddar cheese produced at a dairy is normal with a mean of 11.8 ounces and a standard deviation of 0.2 ounces. (Round all answers to 4 decimal places, if needed.) (a) The probability that a randomly chosen wedge of cheddar cheese is greater than 11.75 is 0.4013 (b) If a sample of 15 is randomly chosen, then the distribution of the sample mean weight is approximately normal + with a mean of 11.8 and a standard deviation of 0.0516 (c) The probability that the sample mean weight of this sample of 15 is less than 11.75 is 0.1660 (d) The probability that the sample mean weight of this sample of 15 is greater than 11.75 is 0.8340 (e) The probability that the sample mean weight of this sample of 15 is between 11.75 and 11.87 is 0.7471 (f) There is only a 7% chance that the average weight of a sample of these 15 cheese wedges will be below 11.72

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