Question

The average production cost for major movies is 69 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 8 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(Correct,Correct)

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 64 and 70 million dollars. Incorrect For the group of 8 movies, find the probability that the average production cost is between 64 and 70 million dollars.

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

Answer 1

a) The distribution of X is ,

b) If , then

Where , and

c) Now ,

From the standard normal probability table Or By using Excel

; "=NORMDIST(0.06,0,1,TRUE)"

; "=NORMDIST(0.28,0,1,TRUE)"

Therefore , the probability that this movie's production cost is between 64 and 70 million dollars is 0.1342.

d) Now ,

From the standard normal probability table Or By using Excel

; "=NORMDIST(0.16,0,1,TRUE)"

; "=NORMDIST(0.79,0,1,TRUE)"

Therefore , the probability that the average production cost is between 64 and 70 million dollars is 0.3488.

e) Yes . the assumption of normal is necessary.