The amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and standard deviation 12 mL. Suppose that 11 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. What is the distribution of

X

?

X

~ N(

,

)

What is the distribution of

¯

x

?

¯

x

~ N(

,

)

If a single randomly selected individual is observed, find the probability that this person consumes is between 67 mL and 71.1 mL.

For the group of 11 pancake eaters, find the probability that the average amount of syrup is between 67 mL and 71.1 mL.

For part d), is the assumption that the distribution is normal necessary? No Yes