The average production cost for major movies is 61 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 17 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible.What is the distribution of XX? XX ~ N(,)What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)For a single randomly selected movie, find the probability that this movie's production cost is between 62 and 66 million dollars.

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Asked Nov 16, 2019
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The average production cost for major movies is 61 million dollars and the standard deviation is 21 million dollars. Assume the production cost distribution is normal. Suppose that 17 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 62 and 66 million dollars. 
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Expert Answer

Step 1
  1. Distribution of X:

For a normal distribution, the distribution of X is N(µ,σ2).

Here, µ=61 and σ=21.

Thus, the distribution of X is obtained as N(61,441), from the below calculations.

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X~N(, =N(61,21 N(61441)

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Step 2
  1. Distribution of X-bar:

The distribution of X-bar is obtained as N(61,5.09), fro...

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XN 21 = N 61 V17 N(61,5.09)

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