The average amount of money spent for lunch per person in the college cafeteria is $6.98 and the standard deviation is $2.13. Suppose that 48 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(Correct,Correct)
2. What is the distribution of xx? xx ~ N(Correct,)
3. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.5689 and $6.9126.
4. For the group of 48 patrons, find the probability that the average lunch cost is between $6.5689 and $6.9126.
5. For part d), is the assumption that the distribution is normal necessary? NoYes