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In: Statistics and Probability

The average amount of money spent for lunch per person in the college cafeteria is $6.63...

The average amount of money spent for lunch per person in the college cafeteria is $6.63 and the standard deviation is $2.54. Suppose that 18 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 $6.812 and $7.3214.
  4. For the group of 18 patrons, find the probability that the average lunch cost is between $6.812 and $7.3214.
  5. For part d), is the assumption that the distribution is normal necessary? NoYes

Can i have an actual step by step how to? Already graded.

Solutions

Expert Solution

Solution-:

Let,X- amount of money spent for lunch per person in the college cafeteria

Given: also

(a) The distribution of X is normal with and

i.e.

(b) For sample,

We know the result If then whre, and

Here, If   then

whre, and

(c) We find, P[that this patron's lunch cost is between $6.812 and $7.3214]

  

  

   ( From Normal Probability Integral table )

Therefore, the required probability is 0.0785.

(d) We ind, P[ that the average lunch cost is between $6.812 and $7.3214 ]

  

  

  

  

   ( From Normal Probability Integral table )

  

Therefore, the required probability is 0.2570.

(e) Yes.

orchestra answered 2 years ago
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