The average amount of money spent for lunch per person in the college cafeteria is $6.99 and the standard deviation is $2.86. Suppose that 8 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 C? ~ ~ N( c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.7732 and $8.0888. d. For the group of 8 patrons, find the probability that the average lunch cost is between $6.7732 and $8.0888. e. For part d), is the assumption that the distribution is normal necessary? O YesO No