Question

The average amount of money spent for lunch per person in the college cafeteria is $6.82 and the standard deviation is $2.99. Suppose that 9 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 $7.585 and $8.7734. 

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