Question

The average production cost for major movies is 59 million dollars and the standard deviation is 20 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.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. For a single randomly selected movie, find the probability that this movie's production cost is between 57 and 59 million dollars.
4. For the group of 14 movies, find the probability that the average production cost is between 57 and 59 million dollars.
5. For part d), is the assumption of normal necessary? NoYes

Answer 1

Given that, mean = 59 million dollars

standard deviation = 20 million dollars

a) X ~ N(59, 20)

b) sample size = 14

Mean and standard deviation of the sampling distribution of sample mean are,

Therefore,

c) We want to find, P(57 < X < 59)

Therefore, required probability is 0.0398

d) sample size = 14, we want to find,

Therefore, required probability is 0.1443

e) Yes, the assumption of normal is necessary.

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