The average amount of money spent for lunch per person in the college cafeteria is $6.89 and the standard deviation is $2.53. Suppose that 45 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 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 $7.0842 and $7.3228.  For the group of 45 patrons, find the probability that the average lunch cost is between $7.0842 and $7.3228. (           ) For part d), is the assumption that the distribution is normal necessary? NoYes

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The average amount of money spent for lunch per person in the college cafeteria is $6.89 and the standard deviation is $2.53. Suppose that 45 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 $7.0842 and $7.3228. 
  4. For the group of 45 patrons, find the probability that the average lunch cost is between $7.0842 and $7.3228. (           )
  5. For part d), is the assumption that the distribution is normal necessary? NoYes
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