The average production cost for major movies is 62 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 36 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible.

What is the distribution of
X
?
X
~ N(
,
)
What is the distribution of
¯
x
?
¯
x
~ N(
,
)
For a single randomly selected movie, find the probability that this movie's production cost is between 61 and 64 million dollars.
For the group of 36 movies, find the probability that the average production cost is between 61 and 64 million dollars.
For part d), is the assumption of normal necessary? NoYes