The amount of syrup that people put on their pancakes is normally distributed with mean 57 mL and standard deviation 7 mL. Suppose that 48 randomly selected people are observed pouring syrup on their...

The amount of syrup that people put on their pancakes is normally distributed with mean 57 mL and standard deviation 7 mL. Suppose that 48 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(,)


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 57.6 mL and 58.3 mL.


4. For the group of 48 pancake eaters, find the probability that the average amount of syrup is between 57.6 mL and 58.3 mL.


5. For part d), is the assumption that the distribution is normal necessary? NoYes