The average amount of money spent for lunch per person in the college cafeteria is $6.18 and the standard deviation is $2.09. Suppose that 47 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 6.18 2.09 b. What is the distribution of ? - N 0.3049 c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.2527 and $6.6152. d. For the group of 47 patrons, find the probability that the average lunch cost is between $6.2527 and $6.6152. e. For part d), is the assumption that the distribution is normal necessary? O Yes No o