The average amount of money spent for lunch per person in the college cafeteria is $5.97 and the standard deviation is $2.3. Suppose that 49 randomly selected lunch patrons are observed. Assume the...

Extracted text: The average amount of money spent for lunch per person in the college cafeteria is $5.97 and the standard deviation is $2.3. Suppose that 49 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 T? ¤ - N( c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $5.57 and $6. d. For the group of 49 patrons, find the probability that the average lunch cost is between $5.57 and $6. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes