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The average production cost for major movies is 67 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 10 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round z-scores to 2 decimal places for use in calculations. Round all other answers to 4 where possible. a. What is the distribution of X? X - N b. What is the distribution of i? - N c. For a single randomly selected movie, find the probability that this movie's production cost is between 66 and 68 million dollars. d. For the group of 10 movies, find the probability that the average production cost is between 66 and 68 million dollars. e. For part d), is the assumption of normal necessary? O Yeso NO 92% of the largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 7 such intitutions, and let X be the number of intitutions that offer distance learning courses. Please show the following answers to 4 decimal places. a. What is the probability that exactly 6 intitutions in this study offer distance learning courses? b. What is the probability that at most 6 intitutions in this study offer distance learning courses? c. What is the probability that at least 6 intitutions in this study offer distance learning courses? d. What is the probability that between 6 and 7 (including 6 and 7) intitutions in this study offer distance learning courses? According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that the person is between 64.7 and 66.1 inches. c. The middle 50% of Martian heights lie between what two numbers? Low: High: inches inches