The average amount of money spent for lunch per person in the college cafeteria is $6.57 and the standard deviation is $2.23. Suppose that 44 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( b. What is the distribution of x? ¤ ~ N(| c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.95 and $7.33. d. For the group of 44 patrons, find the probability that the average lunch cost is between $6.95 and $7.33. e. For part d), is the assumption that the distribution is normal necessary? ONoOYes

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