The average amount of money spent for lunch per person in the college cafeteria is $6.25 and the standard deviation is $2.28. Suppose that 17 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.What is the distribution of X ? X ~ N(6.25,2.28)What is the distribution of ¯x ? ¯x ~ N(,)For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.6005 and $6.927. For the group of 17 patrons, find the probability that the average lunch cost is between $6.6005 and $6.927. For part d), is the assumption that the distribution is normal necessary? NoYes