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 b. What is the distribution of ? N 5.82 ✓.2.5 0.3686 O 0 c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $5.2871 and $5.6314. 0.0514 d. For the group of 46 patrons, find the probability that the average lunch cost is between $5.2871 and $5.6314. 0.2315 X e. For part d), is the assumption that the distribution is normal necessary? No Yes o

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