The average amount of money spent for lunch per person in the college cafeteria is $5.88 and the standard deviation is $2.57. 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. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $4.4062 and $5.3408.
2. For the group of 6 patrons, find the probability that the average lunch cost is between $4.4062 and $5.3408.
3. For part d), is the assumption that the distribution is normal necessary?Yes or No