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StatisticsQ&A LibraryThe 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?Question

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.

- 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?

Step 1

1.

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

Step 2

Step 3

3.

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

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

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