The amount of syrup that people put on their pancakes is normally distributed with mean 60 mL and standard deviation 12 mL. Suppose that 8 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. What is the distribution of XX? XX ~ N(Correct,Correct)   What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) If a single randomly selected individual is observed, find the probability that this person consumes is between 62.4 mL and 67.2 mL.  For the group of 8 pancake eaters, find the probability that the average amount of syrup is between 62.4 mL and 67.2 mL                                 and   is the assumption that the distribution is normal necessary?

Question

The amount of syrup that people put on their pancakes is normally distributed with mean 60 mL and standard deviation 12 mL. Suppose that 8 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

  1. What is the distribution of XX? XX ~ N(Correct,Correct)  
  2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
  3. If a single randomly selected individual is observed, find the probability that this person consumes is between 62.4 mL and 67.2 mL. 
  4. For the group of 8 pancake eaters, find the probability that the average amount of syrup is between 62.4 mL and 67.2 mL                                 and   is the assumption that the distribution is normal necessary? 

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