Assume that farmers' productivity is normally distributed. Farmer-1 produces an average of 85 units of watermelon per day with a standard deviation of 20. Farmer-2 produces watermelon at an average rate of 75 per day with a standard deviation of 21. Using this information above, determine the probability that Farmer-1 will produce more watermelon than Farmer-2 in a week (5 working days). a) 0.6094 b) 0.7094 c) None of the answers are correct d) 0.6794 e) 0.7794

A semi-truck can transport a maximum of 14,950 pounds. Suppose that a load of cargo containing 115 boxes needs to be transported via this semi-truck. Research has shown that the weights of boxes for this type of cargo have a distribution that has a population mean weight of 125 pounds and a population standard deviation of 20 pounds. Based on this information, what is the probability that all 115 boxes can be safely loaded into the semi-truck and transported?

Samples are drawn from a population with mean 144 and standard deviation 43. Each sample has 12 randomly and independently chosen elements. Find the mean, uz, of the distribution of sample means.

The time required to roast a duck may be taken to have a normal distribution with a mean of 45 minutes and standard deviation 12 minutes. The time required to roast a chicken may be taken to have an independent normal distribution with mean 30 minutes and standard deviation 8 minutes. Assume that the oven can only roast one poultry at one time. 0.338 One duck is chosen at random. Find the probability that at least 50 minutes will be required to roast it. (ii) Three randomly chosen ducks are roasted successively in random order. Find the probability that each of them requires more than 45 minutes to roast. 0.15