The average amount of money spent for lunch per person in the college cafeteria is $5.9 and the standard deviation is $2.9. Suppose that 6 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 5:? a": - N([:,:]) c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between 44.4544 44 45.4444. [3 d. For the group of 6 patrons, find the probability that the average lunch cost is between 54.3542 and 55.6462. [j e. For part d), is the assumption that the distribution is normal necessary? Yes\" No