Question

the amount of syrup that people put on their pancakes is normally distributed with mean 57 ml and standard deviation 8 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( , )
b. what is the distribution of \\( \overline{x} \\)? \\( \overline{x} \\) ~ n( , )
c. if a single randomly selected individual is observed, find the probability that the amount of syrup this person consumes is between 54 ml and 55.2 ml.
d. for the group of 15 pancake eaters, find the probability that the average amount of syrup is between 54 ml and 55.2 ml.
e. for part d), is the assumption that the distribution is normal necessary? ◯ no ◯ yes
hint:
some helpful videos:

• finding the sampling distribution +
• finding a probability using the central limit theorem +
• finding value given a probability using the central limit theorem +
• the central limit theorem for sums +

hint

Explanation:

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Answer:

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