The average amount of money spent for lunch per person in the college cafeteria is $5.54 and the standard deviation is $2.64. Suppose that 11 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 5.54 b. What is the distribution of ¤? ¤ - N( c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.186 and $7.284. d. For the group of 11 patrons, find the probability that the average lunch cost is between $6.186 and $7.284. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes o

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Please answer B, C, & D. 

The average amount of money spent for lunch per person in the college
cafeteria is $5.54 and the standard deviation is $2.64. Suppose that 11
randomly selected lunch patrons are observed. Assume the distribution of
money spent is normal, and round all answers to 4 decimal places where
possible.
a. What is the distribution of X? X - N( 5.54
b. What is the distribution of ? ¤ - N(
c. For a single randomly selected lunch patron, find the probability that
this patron's lunch cost is between $6.186 and $7.284.
d. For the group of 11 patrons, find the probability that the average
lunch cost is between $6.186 and $7.284.
e. For part d), is the assumption that the distribution is normal
necessary?
NoO Yes o
Transcribed Image Text:The average amount of money spent for lunch per person in the college cafeteria is $5.54 and the standard deviation is $2.64. Suppose that 11 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 5.54 b. What is the distribution of ? ¤ - N( c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.186 and $7.284. d. For the group of 11 patrons, find the probability that the average lunch cost is between $6.186 and $7.284. e. For part d), is the assumption that the distribution is normal necessary? NoO Yes o
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