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The average score for games played in the NFL is 20.8 and the standard deviation is...

The average score for games played in the NFL is 20.8 and the standard deviation is 9.3 points. 46 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.

  1. What is the distribution of ¯xx¯? ¯xx¯ ~ N( ___ , ____ )
  2. What is the distribution of ∑x∑x? ∑x∑x ~ N( ____ , ____ )
  3. P(¯xx¯ > 19.7432) = _____
  4. Find the 62th percentile for the mean score for this sample size. _____
  5. P(18.8432 < ¯xx¯ < 21.8856) = _____
  6. Q3 for the ¯xx¯ distribution = _____
  7. P(∑x∑x > 986.3872) = _____
  8. For part c) and e), is the assumption of normal necessary? Yes or No _____
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