The average amount of money spent for lunch per person in the college cafeteria is $6.25 and the standard deviation is $2.67. Suppose that 17 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 $6.1986 and $6.5224. For the group of 17 patrons, find the probability that the average lunch cost is between $6.1986 and $6.5224. For part d), is the assumption that the distribution is normal necessary?

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Asked Feb 16, 2020
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The average amount of money spent for lunch per person in the college cafeteria is $6.25 and the standard deviation is $2.67. Suppose that 17 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 $6.1986 and $6.5224. 
  4. For the group of 17 patrons, find the probability that the average lunch cost is between $6.1986 and $6.5224. 
  5. For part d), is the assumption that the distribution is normal necessary?
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Expert Answer

Step 1

1.

The distribution of X is, X~N($6.25, $2.67).

Step 2

Statistics homework question answer, step 2, image 1

Step 3

3.

The probability that one randomly selected patron lunch cost between $6.1986 and $6.5224 is,

Statistics homework question answer, step 3, image 1

Thus ,the probability that one randomly selected patron lunch cost between $6.1986 and $6.5224 is 0.0483.

...

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