The amount of syrup that people put on their pancakes is normally distributed with mean 55 mL and standard deviation 10 mL. Suppose that 15 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 55 10 b. What is the distribution of ? - N( 55 c. If a single randomly selected individual is observed, find the probability that this person consumes is between 57.7 mL and 61.3 mL. 0.1292 d. For the group of 15 pancake eaters, find the probability that the average amount of syrup is between V, 2.5820 v) o o 57.7 ml and 61.3 mL. 0.1396 e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes o

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