The average amount of money spent for lunch per person in the college cafeteria is $7.12 and the standard deviation is $2.47. Suppose that 11 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of xx? xx ~ N(,)
3. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.333 and $7.2354.
4. For the group of 11 patrons, find the probability that the average lunch cost is between $6.333 and $7.2354.
5. For part d), is the assumption that the distribution is normal necessary? NoYes