The average amount of money spent for lunch per person in the college cafeteria is $5.72 and the standard deviation is $2.23. Suppose that 12 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 ~ MED) b. What is the distribution of 5:? 5: ~ N(:H:]) c. For a single randomly selected lunch patron, nd the probability that this patron's lunch cost is between $5.53 and $6.43. [:] d. For the group of 12 patrons, nd the probability that the average lunch cost is between $5.53 and $6.43. [:] HINTS: - X ~ Ni p .a) - :2 ~ N( ,u ,a/ ) . To find P(a