The average amount of money spent for lunch per person in the college cafeteria is $7.37 and the standard deviation is $2.85. Suppose that 16 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal placeswhere possible. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.32 and $7.16.  For the group of 16 patrons, find the probability that the average lunch cost is between $6.32 and $7.16.  For part d), is the assumption that the distribution is normal necessary? NoYes

Question

The average amount of money spent for lunch per person in the college cafeteria is $7.37 and the standard deviation is $2.85. Suppose that 16 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal placeswhere 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 $6.32 and $7.16. 
  4. For the group of 16 patrons, find the probability that the average lunch cost is between $6.32 and $7.16. 
  5. For part d), is the assumption that the distribution is normal necessary? NoYes

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