The average production cost for major movies is 59 million dollars and the standard deviation is 23 million dollars. Assume the production cost distribution is normal. Suppose that 14 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of a? a - N( c. For a single randomly selected movie, find the probability that this movie's production cost is between 53 and 58 million dollars. d. For the group of 14 movies, find the probability that the average production cost is between 53 and 58 million dollars. e. For part d), is the assumption of normal necessary? Yes No

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.