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 13 randomly...

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 13 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible.

What is the distribution of

X
X
?

X
X
~ N(,)

What is the distribution of

¯
x
x¯
?

¯
x
x¯
~ N(,)

For a single randomly selected movie, find the probability that this movie's production cost is between 69 and 75 million dollars.

For the group of 13 movies, find the probability that the average production cost is between 69 and 75 million dollars.

For part d), is the assumption of normal necessary? YesNo