Directions: Read and solve for the following problems. 1. A population consists of the two numbers (7, 8). Consider all possible samples of size 2 that can be drawn with replacement from this population. Find the following: a. The mean of the sampling distribution of means b. The variance of the sampling distribution c. The standard deviation of the sampling distribution of means. d. Illustrate the probability histogram of the sampling distribution of the means. 2. The average number of liters of water that a person consumes in a month is 12 liters. Assume that the standard deviation is 4.5 liters and the distribution is approximately normal. a. Find the probability that a person selected at random consumes more than 13 liters per month. b. If a sample of 20 individuals is selected, find the probability that mean of the sample will be more than 13 liters