1. A population has mean 555 and standard deviation 40. - Find the mean and standard deviation of sample means for samples of size 50. - Find the probability that the mean of a sample of size 50 will be more than 570. 2. A prototype automotive tire has a design life of 38,500 miles with a standard deviation of 2,500 miles. Five such tires are manufactured and tested. On the assumption that the actual population mean is 38,500 miles and the actual population standard deviation id 2,500 miles, find the probability that the sample mean will be less than 35,000 miles. Assume that the distribution of lifetimes of such tires is normal. 3. A normal distributed population has a mean 1,200 and standard deviation 120. - Find the probability that a single randomly selected element X of the population is between 1,100 and 1,300. - Find the mean and standard deviation ofifor samples of size 25. - Find the probability that the mean of a sample of size 25 drawn from this population is between 1,100 and 1,300. 4. Suppose the mean weight of school children's book bags is 17.5 pounds, with standard deviation 2.2 pounds. Find the probability that the mean weight ofa sample of 30 book bags will exceed 18 pounds