Round all answers to 4 decimal places where possible.

Question

The average production cost for major movies is 65 million dollars and the standard deviation is 18 million dollars. Assume the production cost distribution is normal. Suppose that 7 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 ?  ~ N(Correct,)
2. What is the distribution of ?  ~ N(Correct,)
3. For a single randomly selected movie, find the probability that this movie's production cost is between 61 and 64 million dollars. 
4. For the group of 7 movies, find the probability that the average production cost is between 61 and 64 million dollars. 
5. For part d), is the assumption of normal necessary? 

Answer 1

The distribution of X is a normally distributed variable with mean 65 million and standard deviation of 18 million. This is the population distribution.

The distribution of x bar is a normally distributed variable with a mean of 65 million and a standard deviation of 18 million/sqrt(7). This is the sampling distribution.

To find parts c and d, you can use the normalcdf command in your TI84 calculator (or convert the lower and upper bounds to z-scores and use a table)

C: normalcdf(lowerbound = 61, upperbound = 64, mean = 65, sd = 18) = 0.0658

D: C: normalcdf(lowerbound = 61, upperbound = 64, mean = 65, sd = 18/sqrt(7)) = 0.1633

The assumption of normality is not necessary for part D because it was given that the population was normally distributed, thus the sampling distribution of sample size 7 is automatically normally distributed as it flows from the fact that the population is normally distributed.

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