The average amount of money spent for lunch per person in the college cafeteria is $6.3 and the standard deviation is $2.07. 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 ofx?x~ N( , )

C. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $5.4124 and $5.985.

D. For the group of 6 patrons, find the probability that the average lunch cost is between $5.4124 and $5.985.

E. For part d), is the assumption that the distribution is normal necessary?YesNo