The average amount of money spent for lunch per person in the college cafeteria is $5.71 and the standard deviation is $2.99. Suppose that 41 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 $5.7695 and $6.133.
4. For the group of 41 patrons, find the probability that the average lunch cost is between $5.7695 and $6.133.
5. For part d), is the assumption that the distribution is normal necessary? NoYes