The average amount of money spent for lunch per person in the college cafeteria is $5.82 and the standard deviation is $2.5. Suppose that 46 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal placeswhere possible. a. What is the distribution of X? X-N 5.82 ✓ O O ✓, 2.5 ✓0.3686 b. What is the distribution of ? N(5.82 Or c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $5.2871 and $5.6314. d. For the group of 46 patrons, find the probability that the average lunch cost is between $5.2871 and $5.6314. ODNO Yo

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The average amount of money spent for lunch per person in the college cafeteria is $5.82 and the standard
deviation is $2.5. Suppose that 46 randomly selected lunch patrons are observed. Assume the distribution
of money spent is normal, and round all answers to 4 decimal placeswhere possible.
a. What is the distribution of X? X N 5.82
2.5
✓ O O
b. What is the distribution of ? N( 5.82
✓0.3686 ✓ Or Or
c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is
between $5.2871 and $5.6314.
d. For the group of 46 patrons, find the probability that the average lunch cost is between $5.2871 and
$5.6314.
e. For part d), is the assumption that the distribution is normal necessary? No Yes o
Hint:
Hint
Transcribed Image Text:The average amount of money spent for lunch per person in the college cafeteria is $5.82 and the standard deviation is $2.5. Suppose that 46 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal placeswhere possible. a. What is the distribution of X? X N 5.82 2.5 ✓ O O b. What is the distribution of ? N( 5.82 ✓0.3686 ✓ Or Or c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $5.2871 and $5.6314. d. For the group of 46 patrons, find the probability that the average lunch cost is between $5.2871 and $5.6314. e. For part d), is the assumption that the distribution is normal necessary? No Yes o Hint: Hint
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