The average amount of money spent for lunch per person in the college cafeteria is 55.74 and the standard deviation is $2.52. 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 ? - N c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $5.7665 and $6.3244.

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The average amount of money spent for lunch per person in the college cafeteria is $5.74 and the standard
deviation is $2.52. 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-NO
b. What is the distribution of ? I ~ N
c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is
between $5.7665 and $6.3244.
d. For the group of 45 patrons, find the probability that the average lunch cost is between $5.7665 and
$6.3244.
e. For part d), is the assumption that the distribution is normal necessary? Yes No o
Transcribed Image Text:The average amount of money spent for lunch per person in the college cafeteria is $5.74 and the standard deviation is $2.52. 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-NO b. What is the distribution of ? I ~ N c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $5.7665 and $6.3244. d. For the group of 45 patrons, find the probability that the average lunch cost is between $5.7665 and $6.3244. e. For part d), is the assumption that the distribution is normal necessary? Yes No o
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