The average amount of money spent for lunch per person in the college cafeteria is $6.92 and the standard deviation is $2.01. Suppose that 45 randomly selected lunch patrons are observed. Assume the distribution of noney spent is normal, and round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 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 $7.3106 and $7.5704.

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The average amount of money spent for lunch per person in the college cafeteria is $6.92 and the standard
deviation is $2.01. Suppose that 45 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(
b. What is the distribution of a? a - N(
c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between
$7.3106 and $7.5704.
d. For the group of 45 patrons, find the probability that the average lunch cost is between $7.3106 and
$7.5704.
e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes
Transcribed Image Text:The average amount of money spent for lunch per person in the college cafeteria is $6.92 and the standard deviation is $2.01. Suppose that 45 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( b. What is the distribution of a? a - N( c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $7.3106 and $7.5704. d. For the group of 45 patrons, find the probability that the average lunch cost is between $7.3106 and $7.5704. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes
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