Variance = (standard deviation)^2. 1. Suppose a population X is following a normal distribution with a mean of 45 and standard deviation of 3. That is, X~N(45, 32). Suppose there is a sample mean X-bar with samples of size 36. Please follow the 4-step as follows and use the z-table to get the following probabilities in step 4: Solutions: Step 1: Is the distribution of the sample mean X-bar Normal or not? Why? Step 2: What is the mean and standard deviation of the sample mean X-bar? Step 3: Please complete X-bar ~ NC Step 4: Get the following probabilities. , ). a. P(X-bar 43.5) = b. P(X-bar>44) = c. P(43.8