The average production cost for major movies is 59 million dollars and the standard deviation is 19 million dollars. Assume the production cost distribution is normal. Suppose that 6 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. a. What is the distribution of X? X-NO b. What is the distribution of ? NO For ringle randomly colected movie find the probability that this mouic's production cort in

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The average production cost for major movies is 59 million dollars and the standard deviation is 19 million dollars. Assume the production cost distribution is normal. Suppose that 6 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.

a. What is the distribution of \( X \)? \( X \sim N(\text{\_\_\_}, \text{\_\_\_}) \)

b. What is the distribution of \( \bar{X} \)? \( \bar{X} \sim N(\text{\_\_\_}, \text{\_\_\_}) \)

c. For a single randomly selected movie, find the probability that this movie's production cost is between 56 and 59 million dollars. \(\_\_\_\_\_\_\_\_\_\_ \)

d. For the group of 6 movies, find the probability that the average production cost is between 56 and 59 million dollars. \(\_\_\_\_\_\_\_\_\_\_ \)

e. For part d), is the assumption of normal necessary? \( \circ \) Yes \( \circ \) No
Transcribed Image Text:The average production cost for major movies is 59 million dollars and the standard deviation is 19 million dollars. Assume the production cost distribution is normal. Suppose that 6 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. a. What is the distribution of \( X \)? \( X \sim N(\text{\_\_\_}, \text{\_\_\_}) \) b. What is the distribution of \( \bar{X} \)? \( \bar{X} \sim N(\text{\_\_\_}, \text{\_\_\_}) \) c. For a single randomly selected movie, find the probability that this movie's production cost is between 56 and 59 million dollars. \(\_\_\_\_\_\_\_\_\_\_ \) d. For the group of 6 movies, find the probability that the average production cost is between 56 and 59 million dollars. \(\_\_\_\_\_\_\_\_\_\_ \) e. For part d), is the assumption of normal necessary? \( \circ \) Yes \( \circ \) No
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From the provided information,

μ=59,σ=19,n=6

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