The average amount of money spent for lunch per person in the college cafeteria is $7.45 and the standard deviation is $2.12. 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( b. What is the distribution of ? I ~ N( c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $7.1862 and $7.4108. d. For the group of 47 patrons, find the probability that the average lunch cost is between $7. 1862 and $7.4108. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes