The average amount of money spent for lunch per person in the college cafeteria is $6.13 and the standard deviation is $2.2. Suppose that 6 randomly selected lunch patrons are observed. Assume the...

The average amount of money spent for lunch per person in the college cafeteria is $6.13 and the standard deviation is $2.2. 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.

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 $6.45 and $7.64.


4. For the group of 6 patrons, find the probability that the average lunch cost is between $6.45 and $7.64.


5. For part d), is the assumption that the distribution is normal necessary? NoYes