The average production cost for major movies is 58 million dollars and the standard deviation is 23 million dollars. Assume the production cost distribution is normal. Suppose that 38 randomly selected major movies are researched. Answer the following questions. Give your answers ir millions of dollars, not dollars. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 58 b. What is the distribution of ? N 58 - 23 00 3.7311 0 c. For a single randomly selected movie, find the probability that this movie's production cost is between 54 and 57 million dollars. 0.0515 d. For the group of 38 movies, find the probability that the average production cost is between 54 and 57 million dollars. 0.2513 X e. For part d), is the assumption of normal necessary? Yes No