The amount of syrup that people put on their pancakes is normally distributed with mean 59 mL and standard deviation 7 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 x? a - N( c. If a single randomly selected individual is observed, find the probability that this person consumes is between 60.1 mL and 61.8 mL.

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The amount of syrup that people put on their pancakes is
normally distributed with mean 59 mL and standard
deviation 7 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 æ? a - N(
c. If a single randomly selected individual is observed,
find the probability that this person consumes is
between 60.1 mL and 61.8 mL.
d. For the group of 15 pancake eaters, find the
probability that the average amount of syrup is
between 60.1 mL and 61.8 mL.
e. For part d), is the assumption that the distribution is
normal necessary? O Nol
NoO Yes
Transcribed Image Text:The amount of syrup that people put on their pancakes is normally distributed with mean 59 mL and standard deviation 7 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 æ? a - N( c. If a single randomly selected individual is observed, find the probability that this person consumes is between 60.1 mL and 61.8 mL. d. For the group of 15 pancake eaters, find the probability that the average amount of syrup is between 60.1 mL and 61.8 mL. e. For part d), is the assumption that the distribution is normal necessary? O Nol NoO Yes
Expert Solution
Step 1

(a)

Determine the distribution of X.

The distribution of X is obtained below as follows:

Statistics homework question answer, step 1, image 1

 

 

Step 2

(b)

Statistics homework question answer, step 2, image 1

Thus, the value of sample mean of the sampling distribution is 59.

 

The value of the sampling distribution of the standard deviation is,

 

Statistics homework question answer, step 2, image 2

 

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