PLEASE PROVIDE SUPPORTING SOLUTIONS TO YOUR ANSWERS 1. Suppose the mean number of days to germination of a variety of seed is. with standard deviation days. Find the probability that the mean germination time of a sample of seeds will be within day of the population mean. 2. A normally distributed population has mean 57 800 and standard deviation 750. a. Find the probability that a single randomly selected element X ofthe population is between 57,000 and 58,000. b. Find the mean and standard deviation Xof for samples of size 100. c. Find the probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000. 3. Suppose the mean length of time between submission of a state tax retum requesting a refund and the issuance of the refund is 47 days, with standard deviation 6 days. Find the probability that in a sample 50 of retums requesting a refund, the mean such time will be more than 50 days. 4. Suppose the mean weight of school children's book bags is 17.4 pounds. with standard deviation 2.2 pounds. Find the probability that the mean weight of a sample of book bags will exceed 17 pounds. 5. Borachio eats at the same fast food restaurant every day. Suppose X the time between the moment Borachio enters the restaurant and the moment he is served his food is normally distributed with mean 4.2 minutes and standard deviation 1.3 minutes. a. Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is sewed. b. Find the probability that average time until he is served in eight randomly selected visits to the restaurant will be at least 5 minutes. Consider the following probability dittibution. "IE (I) Find p. (b) Find the sampling distribution of the sample mean '2'? for samples of size n = 2. (1:) Show that X - is an unbiased estimator for u