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. For the group of 9 patrons, find the probability that the average lunch cost is between $7.585 and $8.7734.  For part d), is the assumption that the distribution is normal necessary? YesNo

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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. For the group of 9 patrons, find the probability that the average lunch cost is between $7.585 and $8.7734. 
  2. For part d), is the assumption that the distribution is normal necessary? YesNo

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